POEM BY NARI SECOND N = 1

Poem by Nari
visual poetry from the cyberstream

SECOND
N = 1
-
superanalog
of
complex structure

Steven Duplij, Department of Physics,
University of Kaiserslautern,
Postfach 3049, D-67653 Kaiserslautern,
Germany
October 9, 1995
Abstract

We found another N = 1 odd
superanalog
of complex structure
(the even one is widely used in the
theory of super Riemann surfaces).
New N = 1 superconformal-like
transformations are similar to anti-
holomorphic ones of nonsupersymmetric
complex function theory.

They are dual to the ordinary
superconformal transformations subject
to the Berezinian addition formula
presented, noninvertible, highly
degenerated and twist parity of the
tangent space in the standard basis.
They also lead to the "mixed cocycle
condition" which can be used in
building noninvertible objects analogous
to super Riemann surfaces.
A new parametrization for the
superconformal group is presented which
allows us to extend it to a semigroup
and to unify the description of
old and new transformations.

We found another N = 1 odd superanalog... ce is spanned by 1-forms f dZ; d | reduced mappings of two-dimensional (1 es not exist (* (g(z)) = 0;*(f(z)) guage which is more physically transpar PA ~ @ ~ D ! and >d ~ Z; d ~ ent and adequate in constructing object @~ z PT def = 0 ~ @| D~ z ibed by Z = (z; |), where z is an even ns are noninvertible by definition. In coordinate and | is an odd one. The mos the idea is a special class of reduced rdinate z = zbody + zsoul; zbody = * (z o super Riemann surfaces represented as ibility of the even functions f(z) and owing way: 1) the Berezinian exists (z) g(z) < 0, where prime is a differen nsformations [3]. In the local approach tiation by argument (or by z). Therefor e functional definition of superspace ). First type of SA transformations for ts and non-invertible (*(g(z)) 6 = group, while second two types are in an ed Ber > ~ Z=Z< = f 0(z) g(z) + v(z) 0 ( superspace in C 1 j 1 is defined by the and invertible (* (g(z)) 6 = 0;* ( standard basis f @; D g, where D = @| + are in an idea of the semigroup [6] . s in [3]). In these notations the super nsional superconformal field theories [ 2 acts in the tangent and cotangent super D g, where D = @| + |@, @| = @=@| ; = @~ z PT def = 0 ~ @| D~ z. defined by the standard basis f @ ; = 0; * (f(z)) 6 = 0 ) ; 2) the Berezinian ent space matrix PA as @ D ! = 0; * (f(z)) = 0); 3 ) the Berezinian doe | < = > dZ; d| < PA, where PA = s not exist (* (g(z ) ) = 0; * (f(z)) = 0 oordinate language which is more physic a f 0(z) g(z) + v(z) 0 (z) g 2 (z) + | > v case * (g(z)) 6 = 0 for SA transform a ~ Z; d ~ | < = > dZ ; d| < PA, where PA ergroup [5]. Here we consider an altern a |@, @| = @=@|; @ = @ =@z. The dual cotan @ = @=@z. The dual cotangent sp a trix PA as @ D ! = P A ~ @ ~ D ! and > d ex superspace, namely superconformal tr a rmations (see also [ 6] and [7]). We use uing transition functions [3, 4]. From a dimensional supersp a ce C 1 j 1 is descr s the supersymmetry relations a t intriguing peculi a rity of the functio s [9] and can be suitable for physical a existence of soul p a rts in the even coo ody = * (z); zsoul def = z first of a symmetry relations a re D 2 = @; dZ 2 = he even coordinate z = zbody + zsoul; z b peranalog of a Jaco b ian, the Berezinian pplications [10]. Also we exploit the c epresented as colle c tions of open super z) g 2 (z) + | > v(z) g(z) < 0, wher e topology in odd dir e ctions [9] and can ollections of open superdomains the sup e s having new featur e s. Locally (1 j 1)- an even coordinate and | is an odd on e nian exists and inv e rtible (* (g(z)) 6 o superspace [8] which admits existenc e m a sub-group of th e superanalytic semi The idea of superconformal symmetry is e gent space is spann e d by 1-forms f dZ; (or by z). Therefore, we can classi f f super Riemann sur f aces [1] and in two g, where dZ = dz + |d| (the si g dz. The semigroup o f SA transformations rconformal transformations are used as g (1) in the followin g way: 1) the Berezi uperspaces by means of the tan g nformal transformat i ons [3]. In the loc . The most intriguing peculiarity of t h ons are used as glu i ng transition funct re D 2 = @; dZ 2 = dz. The sem i [12], can be determ i ned Ber > ~ Z=Z < = ly (1 j 1)-dimensional superspace C 1 j e reduction, which l eads to new transfo y the transformations (1) in the fol l The idea of superco n formal symmetry is cting objects having new features. Loca l ies [2]. The main a n d fundamental ingre uper Riemann surfaces [1] and in two-di m domains the superco n formal transformati = 0). First type of SA transformatio n ions [3, 4]. From a n other side they app ns as in [3]). In these notatio n rtible by definitio n . In case * (g(z)) , the Berezinian [12], can be determi n -dimensional superc o nformal field theor tions (1) the superanalog of a Jacobia n the functional appr o ach to superspace [ to new transformations (see also [6] a n 6 = 0 for SA transf o rmations (1) the su of nontrivial topology in odd directio n j 1) complex supers p ace, namely superco 0; * (f(z)) = 0); 3) the Berezinian d o al approach to supe r Riemann surfaces r ns f(z) and g(z), because odd functi o we consider an alte r native tangent spac ]. The main and fundamental ingredient o ); zsoul def = z fi r st of all by invert ll by invertibility of the even functi o exists and non-inve r tible (* (g(z)) 6 = mappings of two-dimensional (1 j 1) com p dient of the idea i s a special class of e special reduction of the structure su p n of the structure s upergroup [5]. Here 1 is described by Z = (z; |), where z i s 8] which admits exi s tence of nontrivial group of SA transformations act s be suitable for phy s ical applications [ f(z)) 6 = 0); 2) the Berezinian exi s exceptionally impor t ant in the theory o xceptionally important in the theory of s ear as a result of t he special reductio ive tangent space reduction, which lead s 10]. Also we exploi t the coordinate lan The tangent superspace in C 1 j 1 i s e, we can classify t he transformations tic semigroup, while second two type s spaces by means of t he tangent space ma in the tangent and cotangent s nal definition of s u perspace [8] is the [8] is the existence of soul parts in t g(z), because odd f u nctions are noninve d [7]). We use the functional approach t idea of the semigro u p [6]. The tangent nother side they appear as a result of t d| g , where dZ = d z + |d| (the signs a prime is a differentiation by argumen t lly transparent and adequate in constr u s form a sub-group of the superanal y We found another N = 1 odd superanalog...

______@______.______.__ __________@_________.___

Steven Duplij
Mathematical Physics

Kharkov State University, Ukraine
and
University of Kaiserslautern, Germany

SECOND N=1 SUPERANALOG OF COMPLEX STRUCTURE
alg-geom/9510013, [abs, src, ps]

University of Kaiserslautern preprint KL-TH-95/23, October 1995, 9 p.
Journal of Mathematical Physics, 1997, v. 58, n. 2, February.

Publications
1985 - 1997

(supersymmetry, quantum groups and mathematical physics)

http://gluon.physik.uni-kl.de/~duplij/pubrecnt.htm

______@______.______.__ __________@_________.___

"Could you make a link... to the original article... People can compare input and output..."

, .. . .-. -. >,'', >,color=1 >. . . !! >,, >... .. . >,. . :. ? >, >--,? 1000% >, >; >,. . > > >. .! . 1.' . . 2., ? ,. .. (.../.) . . . . , .

s i l e n c e

ICON
Transparent eyes, Affected tears Call to the soul's bottom Stronger than the Fate. And nothing more to say-- Metamorphoses burn me Embroidering the summons To wash away the Slave. The obstinacy of Nought, The distances got blind... Caressing flowers perished With foam of the dreams. I put on leaves of bliss, I colour lying scaffold In the primordial trace To harden like a mad. Disfiguring Motif I glue up moan with verses, Insatiable words. I grasp with pain of years For roses strongest wish. I have been rotten, staying Alive as Skeleton Of debts to have been gnawed And have already gone.
Surmounting the Night I come to open space, To set for them the Candle Adhered to the hand. The Icon. They: my son And daughter-- stolen By way of life, Landscape, Some trees... And Light...

Steven Duplij
Poetry in English

Kharkov State University, Ukraine
and
University of Kaiserslautern, Germany

http://gluon.physik.uni-kl.de/~duplij/poe-sam.htm

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1997</++++><--> <++++ ----=-2><-></++++> <++++ ----=-1 -----=#707070> (-------------, ------- ------ --- ------------ -------)</++++><--> <++++ ----=-2><-></++++> <++++> <++++ ----=-1> <+ ----="----://-----.------.------.--/~------/--------.---"> <+>----://-----.------.------.--/~------/--------.---</+></+></++++></++++><--> </++++> <-> <--> <-> <--- ---="------.---" ---="---" -----=256 ------=24><--> </++> </++> </+++++> <-> <+++++ -----------=26 -----="98%"> <++> <++ -------=#000000 -----=----- ------=--- -----="30%"> <++++> <++++ ----=-2 -----=#808080> ______@______.______.__<--> __________@_________.___</++++><--> <-> <--> <-> <++++ ----=-1 -----=#707070> &----;+----&----;---<--> ----&----;-&----;----...<--> --&----;---&----;--------<--> -------...<--> +-----&----;---<--> -------&----;-----<--> ---&----;------...&----;</++++><--> </++++> <++++++><++++ ----=-2 -----=#000000>_</++++></++++++><--> </++> <++ -------=#000000 -----=---- ------=--- -----="70%"> <++++> <++++ ----=-2 -----=#606060> ,<++++ -----=#404040></++++><--> ..<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> .-.<++++ -----=#404040></++++><--> -.<++++ -----=#404040></++++><--> &--;,'',<++++ -----=#404040></++++><--> &--;,-----=1<++++ -----=#404040></++++><--> &--;.<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> !!<++++ -----=#404040></++++><--> &--;,,<++++ -----=#404040></++++><--> &--;...<++++ -----=#404040></++++><--> ..<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> &--;,.<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> :.<++++ -----=#404040></++++><--> ?<++++ -----=#404040></++++><--> &--;,<++++ -----=#404040></++++><--> &--;--,?<++++ -----=#404040></++++><--> 1000%<++++ -----=#404040></++++><--> &--;,<++++ -----=#404040></++++><--> &--;;<++++ -----=#404040></++++><--> &--;,.<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> &--;<++++ -----=#404040></++++><--> &--;<++++ -----=#404040></++++><--> &--;.<++++ -----=#404040></++++><--> .!<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> 1.'<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> 2.,<++++ -----=#404040></++++><--> ?<++++ -----=#404040></++++><--> ,.<++++ -----=#404040></++++><--> ..<++++ -----=#404040></++++><--> (.../.)<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++><--> ,<++++ -----=#404040></++++><--> .<++++ -----=#404040></++++></++++><--> </++++> <-> <--> <-> <--> <-> <--- ---="-------.---" ---="-------" -----=410 ------=205><--> <++++ ----=-2><-></++++> <++++ ----=-1 -----=#707070> - - - - - - -</++++><--> <-> <--> <-> <++++> <++++ -----=#909090> <+>++++</+></++++><--> <++++ ----=-2><-></++++> <++++ -----=#808080> +---------- ----,<--> +------- -----<--> +--- -- --- ----'- ------<--> +------- ---- --- +---.<--> +-- ------- ---- -- -----<--> +------------ ---- --<--> +----------- --- -------<--> +- ---- ---- --- +----.<--> +-- --------- -- +-----,<--> +-- --------- --- -----...<--> +-------- ------- --------<--> +--- ---- -- --- ------.<--> + --- -- ------ -- -----,<--> + ------ ----- --------<--> +- --- ---------- -----<--> +- ------ ---- - ---.<--> +---------- +----<--> + ---- -- ---- ---- ------,<--> +--------- -----.<--> + ----- ---- ---- -- -----<--> +-- ----- --------- ----.<--> + ---- ---- ------, -------<--> +---- -- +-------<--> +- ----- -- ---- ---- ------<--> +-- ---- ------- ----.<--> <++++ ----=-2><-></++++> +---------- --- +----<--> + ---- -- ---- -----,<--> +- --- --- ---- --- +-----<--> +------ -- --- ----.<--> +-- +---. +---: -- ---<--> +-- ---------- ------<--> +- --- -- ----,<--> +--------,<--> +--- -----...<--> +-- +----...</++++><--> </++++> <-> <--> <-> <--> <-> <++++ -----=#808080> <++++ ----=+1 -----=#+0+0+0> +----- +-----</++++><--> <++++ -----=#909090> +----- -- +------</++++><--> <++++ ----=-2><-></++++> <++++ ----=-1 -----=#707070> <+>+------ +---- +---------, +------</+><--> <++++ ----=-1>---</++++><--> <+>+--------- -- +-------------, +------</+></++++><--> <++++ ----=-2><-></++++> <++++> <++++ ----=-1> <+ ----="----://-----.------.------.--/~------/-------.---"> <+>----://-----.------.------.--/~------/-------.---</+></+></++++></++++><--> </++++> <-> <--> <-> <--- ---="------.---" ---="---" -----=256 ------=24><--> </++> </++> </+++++> <-> <--> <-> <++++ ----=-2 -----=#707070> +-------- &----; 1997 +----- +-----. +-- ------ --------.</++++><--> <++++ ----=-1> <+ ----="------:------@------.------.--">------@------.------.--</+></++++><--> <++++ ----=-2><-></++++> <++++ ----=-2 -----=#707070> +-------- &----; 1997 +--- -- +---. +-- ------ --------.</++++><--> <-> <--> <-> <+ ----="--_----.----"> <--- ---="---1.---" ---="---" -----=40 ------=40 ------=0></+><--> </++++++> <-> <--> <-> <! ------------------------------> <+++++ -----------=26 -----="98%"> <++> <++ -------=#000000 -----=---- ------=--- -----="100%"> <++++ ----=-2 -----=#606060><+++> SECOND SECOND N = 1 </+++></++++> </++> </++> </+++++> <-> <++++ ----=-2 -----=#707070> ----------- -- --- -------</++++><--> <-> <--> <-> <+ ----="--_----.----"> <--- ---="---1.---" ---="---" -----=40 ------=40 ------=0></+><--> <! ----------------------------------------------------------------> </++++++> <-> <--> <-> </++++> </++++>

realization is the meaning