English
Related papers

Related papers: Semidualizing DG Modules over Tensor Products

200 papers

We give a construction of Gorenstein projective $\tau$-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $\tau$-tilting…

Representation Theory · Mathematics 2022-01-13 Zhi-Wei Li , Xiaojin Zhang

We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.

Representation Theory · Mathematics 2007-05-23 P P Martin , S Ryom-Hansen

Tensor products usually have nonzero torsion. This is a central theme of Auslander's paper "Modules over unramified regular local rings"; the theme continues in the work of Huneke and Wiegand. The main focus in this note is on tensor powers…

Commutative Algebra · Mathematics 2014-12-22 Olgur Celikbas , Srikanth B. Iyengar , Greg Piepmeyer , Roger Wiegand

It is shown that the Gelfand--Kirillov dimension for modules over quantum Laurent polynomials is tensor-minimal. The Brookes--Groves invariant associated with a tensor product of modules is determined. It is also shown that there can be…

Rings and Algebras · Mathematics 2011-11-18 Ashish Gupta

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

Quantum Algebra · Mathematics 2007-06-13 Igor Frenkel , Mikhail Khovanov , Catharina Stroppel

Following work of Brundan and Kleshchev (2000), which considered tensor products with the natural module (and its dual) for $\text{GL}(n)$, we take the next fundamental module and explore the relationship between multiplicities of…

Representation Theory · Mathematics 2024-10-07 Miriam G Norris

We give a detailed survey of the theory of quasidiagonal C*-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and…

Operator Algebras · Mathematics 2007-05-23 Nathanial P. Brown

In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of formal deformation modules which are cohomologically…

Algebraic Geometry · Mathematics 2011-03-08 Francois Petit

In this paper we study the tensor category structure of the module category of the restricted quantum enveloping algebra associated to $\mathfrak{sl}_2$. Indecomposable decomposition of all tensor products of modules over this algebra is…

Quantum Algebra · Mathematics 2010-10-04 Hiroki Kondo , Yoshihisa Saito

This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…

Representation Theory · Mathematics 2007-11-26 Axel Boldt , Ahmad Mojiri

In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We…

q-alg · Mathematics 2008-02-03 Yi-Zhi Huang

This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir arXiv:0905.2621. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between…

Category Theory · Mathematics 2023-08-04 Leonid Positselski

We show that the set $\s(R)$ of shift-isomorphism classes of semidualizing complexes over a local ring $R$ admits a nontrivial metric. We investigate the interplay between the metric and several algebraic operations. Motivated by the dagger…

Commutative Algebra · Mathematics 2007-05-23 Anders Frankild , Sean Sather-Wagstaff

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

Commutative Algebra · Mathematics 2009-11-11 Luchezar L. Avramov , Ragnar-Olaf Buchweitz , Srikanth Iyengar

We show there exist no nontrivial semidualizing modules for nonmodular rings of invariants of order $p^n$ with $p$ a prime.

Commutative Algebra · Mathematics 2014-08-26 William Sanders

Tensor product of highest weight modules and intermediate modules for Virasoro algebra have been studied around 1997. Since then the irreducibility problem for tensor product of modules is open. We consider the loop-Virasoro algebra $Vir…

Representation Theory · Mathematics 2021-12-28 Priyanshu Chakraborty , Punita Batra

Let $A$ be a hereditary algebra over an algebraically closed field $k$ and $A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$, we denote by $\delta (T)$ the number of non isomorphic indecomposable summands of $T$.…

Representation Theory · Mathematics 2013-01-24 Shunhua Zhang

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

On the tensor product of two homotopy Gerstenhaber algebras we construct a Hirsch algebra structure which extends the canonical dg algebra structure. Our result applies more generally to tensor products of "level 3 Hirsch algebras" and also…

Algebraic Topology · Mathematics 2011-12-06 Matthias Franz

We survey some results on tensor products of irreducible Harish-Chandra bimodules. It turns out that such tensor products are semisimple in suitable Serre quotient categories. We explain how to identify the resulting semisimple tensor…

Representation Theory · Mathematics 2014-04-29 Victor Ostrik