Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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The Structure of Walled Signed Brauer Algebras

  • Received : 2014.01.20
  • Accepted : 2014.09.19
  • Published : 2016.12.23
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Abstract

In this paper, a new class of diagram algebras which are subalgebras of signed brauer algebras, called the Walled Signed Brauer algebras denoted by ${\overrightarrow{D}}_{r,s}(x)$, where $r,s{\in}{\mathbb{N}}$ and x is an indeterminate are introduced. A presentation of walled signed Brauer algebras in terms of generators and relations is given. The cellularity of a walled signed Brauer algebra is established. Finally, ${\overrightarrow{D}}_{r,s}(x)$, is quasi- hereditary if either the characteristic of a field, say p, p = 0 or p > max(r, s) and either $x {\neq}0$ or x = 0 and $r{\neq}s$.

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