• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1047-1067
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• 2016

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 $r{\neq}s$.