Endomorphism Algebras and q-Traces
Run-Qiang Jian

TL;DR
This paper introduces new algebra structures on graded endomorphisms of quantum symmetric algebras for braided vector spaces of Hecke type, leading to a novel trace related to quantum traces in type A.
Contribution
It constructs three associative algebra structures on endomorphisms of quantum symmetric algebras and defines a new trace that generalizes quantum traces for specific representations.
Findings
Defined three algebra structures on graded endomorphisms.
Constructed a new trace as an algebra morphism.
Connected the trace to quantum traces in type A.
Abstract
For a braided vector space with braiding of Hecke type, we introduce three associative algebra structures on the space of graded endomorphisms of the quantum symmetric algebra . We use the second product to construct a new trace. This trace is an algebra morphism with respect to the third product. In particular, when is the fundamental representation of and is the action of the -matrix, this trace is a scalar multiple of the quantum trace of type .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra
