The Structure of Walled Signed Brauer Algebras

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 −→ D r,s ( x ) ; where r; s ∈ 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, −→ D r,s ( x ) ; is quasi- hereditary if either the characteristic of a (cid:12)eld, say p; p = 0 or p > max ( r; s ) and either x ̸ = 0 or x = 0 and r ̸ = s: