The Structure of Walled Signed Brauer Algebras
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In this paper, a new class of diagram algebras which are subalgebras of signed brauer algebras, called the Walled Signed Brauer algebras denotedby $\overrightarrow{D}_{r,s}(x),$ where $r,s \in \mathbb{N}$ and $x$ is an indeterminate are introduced. A presentation of walled signed Braueralgebras 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 $r \neq s.$
Abstract
In this paper, a new class of diagram algebras which are subalgebras of signed brauer algebras, called the Walled Signed Brauer algebras denotedby $\overrightarrow{D}_{r,s}(x),$ where $r,s \in \mathbb{N}$ and $x$ is an indeterminate are introduced. A presentation of walled signed Braueralgebras 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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