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For each natural number n greater than 1, we define an algebra satisfying many properties that one might expect to hold for a Brauer algebra of type Cn. The monomials of this algebra correspond to scalar multiples of symmetric Brauer…

Representation Theory · Mathematics 2015-03-17 Arjeh M. Cohen , Shoumin Liu , Shona Yu

Motivated by Brundan-Kleshchev's work on higher Schur-Weyl duality, we establish mixed Schur-Weyl duality between general linear Lie algebras and cyclotomic walled Brauer algebras in an arbitrary level. Using weakly cellular bases of…

Quantum Algebra · Mathematics 2015-09-22 Hebing Rui , Linliang Song

We introduce two families of diagrammatic monoidal supercategories. The first family, depending on an associative superalgebra, generalizes the oriented Brauer category. The second, depending on an involutive superalgebra, generalizes the…

Representation Theory · Mathematics 2025-06-13 Saima Samchuck-Schnarch , Alistair Savage

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

Representation Theory · Mathematics 2020-02-17 Kieran Calvert

In this article, we provide a comprehensive characterization of invariants of classical Lie superalgebras from the super-analog of the Schur-Weyl duality in a unified way. We establish $\mathfrak{g}$-invariants of the tensor algebra…

Representation Theory · Mathematics 2024-11-27 Yang Luo , Yongjie Wang

We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to…

Representation Theory · Mathematics 2007-05-23 Mikhail Antipov

This paper introduces monoidal (super)categories resembling the Brauer category. For all categories, we can construct bases of the hom-spaces using Brauer diagrams. These categories include the Brauer category, its deformation the…

Representation Theory · Mathematics 2024-06-27 Sigiswald Barbier

The Brauer algebra has a basis of diagrams and these generate a monoid $H$ consisting of scalar multiples of diagrams. Following a recent paper by Kudryavtseva and Mazorchuk, we define and completely determine three types of conjugation in…

Representation Theory · Mathematics 2009-11-30 Armin Shalile

In this paper, we will define the Brauer algebras of Weyl types, and describe some propositions of these algebras. Especially, we prove the result of type $G_2$ to accomplish our project of Brauer algebras of non-simply laced types.

Representation Theory · Mathematics 2015-03-09 Shoumin Liu

By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a…

Rings and Algebras · Mathematics 2026-01-29 Yuming Liu , Bohan Xing

This is not standard in the sense that we understand a Springer map to be a collapsing of homogeneous bundles. Apart from that we use mostly techniques from Chriss and Ginzbergs book but we work in the equivariant derived category of…

Representation Theory · Mathematics 2013-08-14 Julia Sauter

In 2017, Green and Schroll introduced a generalization of Brauer graph algebras which they call Brauer configuration algebras. In the present paper, we further generalize Brauer configuration algebras to fractional Brauer configuration…

Representation Theory · Mathematics 2025-07-08 Nengqun Li , Yuming Liu

We define a new $q$-deformation of Brauer's centralizer algebra which contains Hecke algebras of type $A$ as unital subalgebras. We determine its generic structure as well as the structure of certain semisimple quotients. This is expected…

Quantum Algebra · Mathematics 2012-08-14 Hans Wenzl

We develop a diagrammatic approach to the representation theory of the quantum symmetric pairs corresponding to orthosymplectic Lie superalgebras inside general linear Lie superalgebras. Our approach is based on the disoriented skein…

Quantum Algebra · Mathematics 2026-05-07 Hadi Salmasian , Alistair Savage , Yaolong Shen

We describe (braided-)commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over…

Category Theory · Mathematics 2010-05-26 Alexei Davydov , Vyacheslav Futorny

We survey results on multiserial algebras, special multiserial algebras and Brauer configuration algebras. A structural property of modules over a special multiserial algebra is presented. Almost gentle algebras are introduced and we…

Representation Theory · Mathematics 2017-03-07 Edward L. Green , Sibylle Schroll

We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…

Representation Theory · Mathematics 2021-12-20 Matthew Westaway

We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de Rham cohomology. We show that the duality…

dg-ga · Mathematics 2008-02-03 Johannes Huebschmann

We show that the algebras describing blocks of the category of cuspidal weight (respectively generalized weight) $\mathfrak{sl}_n$-modules are one-parameter (respectively multi-parameter) deformations of certain Brauer tree algebras. We…

Representation Theory · Mathematics 2011-09-08 Volodymyr Mazorchuk , Catharina Stroppel

The diagram algebra introduced by Brauer that describes the centralizer algebra on tensor products of the natural representation of an orthogonal group has a presentation by generators and relations that only depends on the graph of type An…

Representation Theory · Mathematics 2007-05-23 Arjeh M Cohen , Bart Frenk , David Wales