Gradings on walled Brauer algebras and Khovanov’s arc algebra

By Jonathan Brundan, C. Stroppel. 2011

129 citations recorded by the source corpus.

Abstract We introduce some Z -graded versions of the walled Brauer algebra B r , s ( δ ) , working over a field of characteristic zero. This allows us to prove that B r , s ( δ ) is Morita equivalent to an idempotent truncation of a certain infinite dimensional version of Khovanov’s arc algebra. We deduce that the walled Brauer algebra is Koszul whenever δ ≠ 0 .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5d366dcf370e309f13a1be5f4b0421f675aa94d0

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In Algebra and Number Theory

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Citations in the corpus

Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “This Khovanov algebra also allows us, [32], to mimic (with some effort) the approach from [21] to construct a graded version of the Brauer algebra Brd(δ) for an arbitrary integral parameter δ.”
Deligne Categories and the Limit of Categories Rep(GL(m|n)) (2015, background): “ibe the kernel N⊂T of the surjection T։Pk(λ) choose a basis ψi in M min(p,q)≥s≥p+q−k 2 Hom(Xp,q t ,X p−s,q−s t ). We can choose this basis from the diagram bases for these walled Brauer algebras (see [BS] or [CW]). First, we show that N= T∩ \ i Kerψi The inclusion ⊂is obvious, so we only need to pro”
A basis theorem for the affine oriented Brauer category and its cyclotomic quotients (2014, background): “of "and scopies of #, B r;s() := End OB()(" r#s) (1.1) is the well-known walled Brauer algebra which was introduced independently by Turaev [T1] and Koike [Ko] in the late 1980s; see e.g. [BS]. By analogy with this, 2010 Mathematics Subject Classication: 17B10, 18D10. First author supporte”