Poisson-Lie T-dual sigma models on supermanifolds

We investigate Poisson-Lie symmetry for T-dual sigma models on supermanifolds in general and on Lie supergroups in particular. We show that the integrability condition on this super Poisson-Lie symmetry is equivalent to the super Jacobi identities of the Lie super-bialgebras. As examples we consider models related to four dimensional Lie super-bialgebras $((2A1,1 + 2A)^1, D10_p=1/2)$ and $((2A1,1 + 2A)^1, I)$. Then generally it is shown that for Abelian case (g, I) the super Poisson-Lie T-duality transforms the role of fermionic (bosonic) fields in the model to bosonic (fermionic) fields on the dual model and vice versa.Comment: 13 pages, Revised and accepted for publication in JHE

Super Poisson-Lie symmetry of the GL(1|1) WZNW model and worldsheet boundary conditions

We show that the WZNW model on the Lie supergroup GL(1|1) has super Poisson-Lie symmetry with the dual Lie supergroup B + A + A1;1|.i. Then, we discuss about D-branes and worldsheet boundary conditions on supermanifolds, in general, and obtain the algebraic relations on the gluing supermatrix for the Lie supergroup case. Finally, using the supercanonical transformation description of the super Poisson-Lie T-duality transformation, we obtain formula for the description of the dual gluing supermatrix, then, we find the gluing supermatrix for the WZNW model on GL(1|1) and its dual model. We also discuss about different boundary conditions.Comment: 19 pages, two Refs. have adde

On Artinianness of Formal Local Cohomology, Colocalization and Coassociated Primes

This paper at first concerns some criteria on Artinianness and vanishing of formal local cohomology modules. Then we consider the cosupport and the set of coassociated primes of these modules more precisely.Comment: 12 pages, to appear in Journal Math. Scand.. Some theorems have been adde

On an endomorphism ring of local cohomology

Let $I$ be an ideal of a local ring $(R,\mathfrak m)$ with $d = \dim R.$ For the local cohomology module $H^i_I(R)$ it is a well-known fact that it vanishes for $i > d$ and is an Artinian $R$-module for $i = d.$ In the case that the Hartshorne-Lichtenbaum Vanishing Theorem fails, that is $H^d_I(R) \not= 0,$ we explore its fine structure. In particular, we investigate its endomorphism ring and related connectedness properties. In the case $R$ is complete we prove - as a technical tool - that $H^d_I(R) \simeq H^d_{\mathfrak m}(R/J)$ for a certain ideal $J \subset R.$ Thus, properties of $H^d_I(R)$ and its Matlis dual might be described in terms of the local cohomology supported in the maximal ideal.Comment: 8 pages, The paper will appear in Journal "Communications in Algebra