Koszul duality and Frobenius structure for restricted enveloping algebras
Simon Riche
TL;DR
This paper investigates the relationship between Koszul grading and Frobenius algebra structure in the restricted enveloping algebra of a semisimple Lie algebra over a field of large positive characteristic, addressing a question by W. Soergel.
Contribution
It establishes the compatibility between Koszul grading and Frobenius structure in the restricted enveloping algebra, providing new insights into their interplay.
Findings
Confirmed the compatibility between Koszul grading and Frobenius structure.
Answered a question posed by W. Soergel regarding this compatibility.
Enhanced understanding of algebraic structures in modular representation theory.
Abstract
Let g be the Lie algebra of a connected, simply connected semisimple algebraic group over an algebraically closed field of sufficiently large positive characteristic. We study the compatibility between the Koszul grading on the restricted enveloping algebra (Ug)_0 of g constructed in a previous paper, and the structure of Frobenius algebra of (Ug)_0. This answers a question raised to the author by W. Soergel.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology