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Related papers: Self-injective algebras under derived equivalences

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A different proof to a known criterion of derived equivalence implying birationality is given. Derived equivalent smooth projective curves over an algebraically closed field are proved to be isomorphic. A different proof of derived…

Algebraic Geometry · Mathematics 2011-08-10 Yu-Han Liu

We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

Quantum Algebra · Mathematics 2007-05-23 Pavel Kolesnikov

In this paper we study the category of finitely generated modules over a right $3$-Nakayama artin algebra. First we give a characterization of right $3$-Nakayama artin algebras and then we give a complete list of non-isomorphic finitely…

Representation Theory · Mathematics 2018-05-14 Alireza Nasr-Isfahani , Mohsen Shekari

We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the base field has an odd characteristic. This assumption on the characteristic is for…

Representation Theory · Mathematics 2017-07-03 Susumu Ariki , Ryoichi Kase , Kengo Miyamoto , Kentaro Wada

A double algebra is a linear space $V$ equipped with linear map $V\otimes V\to V\otimes V$. Additional conditions on this map lead to the notions of Lie and associative double algebras. We prove that simple finite-dimensional Lie double…

Quantum Algebra · Mathematics 2018-10-31 M. E. Goncharov , P. S. Kolesnikov

The paper concerns extra special associative algebras, an analogue of the Heisenberg Lie algebra. In particular, we say that an associative algebra is extra special if its center is equal to its derived ideal and the center is…

Rings and Algebras · Mathematics 2022-12-06 Erik Mainellis

We give a complete derived equivalence classification of all symmetric algebras of domestic representation type over an algebraically closed field. This completes previous work by R. Bocian and the authors, where in this paper we solve the…

Representation Theory · Mathematics 2007-05-23 Thorsten Holm , Andrzej Skowronski

In this paper, we introduce $\Phi$-Auslander-Yoneda algebras in a triangulated category with $\Phi$ a parameter set in $\mathbb N$, and provide a method to construct new derived equivalences between these $\Phi$-Auslander-Yoneda algebras…

Representation Theory · Mathematics 2010-02-23 Wei Hu , Changchang Xi

In this paper, our primary focus is on investigating the extension dimensions of syzygy module categories associated with Artin algebras, particularly under various equivalences. We demonstrate that, for sufficiently large $i$, the $i$-th…

Representation Theory · Mathematics 2026-05-08 Junling Zheng , Lulu Tian , Qianyu Shu

A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…

Mathematical Physics · Physics 2013-04-17 David J. Foulis , Sylvia Pulmannova

We complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to…

Representation Theory · Mathematics 2010-09-08 Thorsten Holm , Andrzej Skowronski

In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra $A$ such that $A_0$ has finite global…

Representation Theory · Mathematics 2012-01-27 Kota Yamaura

We work over a perfect field. Recent work of the third-named author established a Derived Auslander Correspondence that relates finite-dimensional self-injective algebras that are twisted $3$-periodic to algebraic triangulated categories of…

Representation Theory · Mathematics 2026-05-13 Gustavo Jasso , Bernhard Keller , Fernando Muro

We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on some classes of associative algebras, including unital algebras, the semigroup algebras of rectangular bands, algebras with enough…

Rings and Algebras · Mathematics 2025-10-22 Mykola Khrypchenko

A finite-dimensional Lie algebra is called (symmetric) self-dual, if it possesses an invariant nondegenerate (symmetric) bilinear form. Symmetric self-dual Lie algebras have been studied by Medina and Revoy, who have proven a very useful…

High Energy Physics - Theory · Physics 2009-10-28 JM Figueroa-O'Farrill , S Stanciu

We describe an infinite-dimensional algebra of hidden symmetries for the self-dual gravity equations. Besides the known diffeomorphism-type symmetries (affine extension of w(infinity) algebra), this algebra contains new hidden symmetries,…

High Energy Physics - Theory · Physics 2009-10-30 A. D. Popov , M. Bordemann , H. Roemer

In The factorization of the Giry monad (arXiv:1707.00488v2) the author considers two $\sigma$-algebras on convex spaces of functions to the unit interval. One of them is generated by the Boolean subobjects and the other is the…

Category Theory · Mathematics 2018-09-05 Tomas Crhak

In this paper we prove that every recursively presented Lie algebra over a field which is a finite extention of its simple subfield can be embedded in a recursively presented Lie algebra defined by relations which are equalities of…

Rings and Algebras · Mathematics 2011-01-25 E. Chibrikov

We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander-Reiten translates. As a result, we prove that…

Representation Theory · Mathematics 2025-08-06 David Nkansah

Let $\Lambda$ be a radical square zero Nakayama algebra with $n$ simple modules and let $\Gamma$ be the Auslander algebra of $\Lambda$. Then every indecomposable direct summand of a tilting $\Gamma$-module is either simple or projective.…

Representation Theory · Mathematics 2020-10-15 Xiaojin Zhang