Affine walled Brauer-Clifford superalgebras
Mengmeng Gao, Hebing Rui, Linliang Song, Yucai Su

TL;DR
This paper introduces affine walled Brauer-Clifford superalgebras over arbitrary domains, proves their freeness and structure, and establishes isomorphisms with previously defined superalgebras, advancing the algebraic understanding of these structures.
Contribution
It constructs and analyzes affine walled Brauer-Clifford superalgebras, proves their freeness, and relates them to existing superalgebras, providing new structural insights.
Findings
$BC_{r, t}^{ m aff}$ is free over $R$ with infinite rank.
Finite-dimensional irreducible modules factor through cyclotomic quotients.
$BC_{k, r, t}$ is free over $R$ if and only if admissible.
Abstract
In this paper, a notion of affine walled Brauer-Clifford superalgebras is introduced over an arbitrary integral domain containing . These superalgebras can be considered as affinization of walled Brauer superalgebras in \cite{JK}. By constructing infinite many homomorphisms from to a class of level two walled Brauer-Clifford superagebras over , we prove that is free over with infinite rank. We explain that any finite dimensional irreducible -module over an algebraically closed field of characteristic not factors through a cyclotomic quotient of , called a cyclotomic (or level ) walled Brauer-Clifford superalgebra . Using a previous method on cyclotomic walled Brauer algebras in \cite{RSu1}, we prove that is…
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons
