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Related papers: Extensions of modules for twisted current algebras

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We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…

Rings and Algebras · Mathematics 2013-12-17 Erhard Neher , Arturo Pianzola

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

Representation Theory · Mathematics 2025-06-05 Haibo Chen , Yucai Su , Yukun Xiao

This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In…

Quantum Algebra · Mathematics 2015-03-13 Fei Kong , Haisheng Li , Shaobin Tan , Qing Wang

Since 2020, finite weight modules have been studied over twisted affine Lie superalgebras. To complete the characterization of modules over affine Lie superalgebras, we need some information regarding modules over untwisted affine Lie…

Representation Theory · Mathematics 2024-11-27 Asghar Daneshvar , Hajar Kiamehr , Maryam Yazdanifar , Malihe Yousofzadeh

Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted…

q-alg · Mathematics 2008-02-03 Chongying Dong , Haisheng Li , Geoffrey Mason

The paper is to classify irreducible integrable modules for the twisted full toroidal Lie algebra with some technical conditions. The twisted full toroidal Lie algebra are extensions of multiloop algebra twisted by sevaral finite order…

Representation Theory · Mathematics 2015-09-10 S. Eswara Rao , Punita Batra

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…

Quantum Algebra · Mathematics 2007-05-23 Benjamin Doyon , James Lepowsky , Antun Milas

In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of…

Quantum Algebra · Mathematics 2012-04-24 Alexei Davydov

We introduce a notion of a (V,T)-module over a vertex algebra V for an arbitrary positive integer T, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A^{T}_{m}(V) for…

Quantum Algebra · Mathematics 2016-03-07 Kenichiro Tanabe

Let $A$ be a connected commutative $\C$-algebra with derivation $D$, $G$ a finite linear automorphism group of $A$ which preserves $D$, and $R=A^G$ the fixed point subalgebra of $A$ under the action of $G$. We show that if $A$ is generated…

Quantum Algebra · Mathematics 2013-12-18 Kenichiro Tanabe

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from X to g. Examples include generalized current algebras and (twisted)…

Representation Theory · Mathematics 2012-02-28 Ghislain Fourier , Tanusree Khandai , Deniz Kus , Alistair Savage

We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from…

Rings and Algebras · Mathematics 2016-04-08 Jeffrey Pike , Alistair Savage

We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the…

Representation Theory · Mathematics 2015-04-14 Angelo Bianchi , Adriano Moura

We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form…

Group Theory · Mathematics 2026-05-08 Egor Voronetsky

In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sums.

q-alg · Mathematics 2008-02-03 Shun-Jen Cheng , Victor Kac , Minoru Wakimoto

In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod $p$ formula for the twisted Alexander polynomial of a knot in the $3$-sphere associated…

Geometric Topology · Mathematics 2026-05-14 Katsumi Ishikawa , Takayuki Morifuji , Masaaki Suzuki

The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl…

Representation Theory · Mathematics 2012-12-18 Vyjayanthi Chari , Ghislain Fourier , Prasad Senesi

We study the Ext modules in the category of left modules over a twisted algebra of a finite quiver over a ringed space $(X,\mathcal O_X)$, allowing for the presence of relations. We introduce a spectral sequence which relates the Ext…

Representation Theory · Mathematics 2019-12-02 Claudio Bartocci , Ugo Bruzzo , Claudio L. S. Rava

Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules…

Quantum Algebra · Mathematics 2021-03-05 Bojko Bakalov , Samantha Kirk

We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…

High Energy Physics - Theory · Physics 2009-10-30 J. Fuchs , C. Schweigert