TL;DR
This paper provides a geometric realization of quantum GL(n) algebras using double partial flag varieties, revealing that their differences stem from a cocycle twist in multiplication.
Contribution
It introduces a geometric approach to quantum GL(n) algebras and explains the algebraic differences via cocycle twisting.
Findings
Realization of quantum GL(n) via double partial flag varieties
Identification of the difference as a cocycle twist
Connection between geometric and algebraic structures
Abstract
The quantum GL(n) of Faddeev-Reshetikhin-Takhtajan and Dipper-Donkin are realized geometrically by using double partial flag varieties. As a consequence, the difference of these two Hopf algebras is caused by a twist of a cocycle in the multiplication.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra