2012•Algebra ColloquiumRequires access

Quiver Hecke Algebras and 2-Lie Algebras

Raphaël Rouquier

Abstract

We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting monoidal categories, which have a geometric description via quiver varieties, in certain cases. We present basic properties of 2-representations and describe simple 2-representations, via cyclotomic quiver Hecke algebras, and through microlocalized quiver varieties.

About this research paper

What this paper is about

Why it matters

OpenAlex reports 146 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Quiver, Mathematics, Pure mathematics, Representation theory, Hecke operator, Simple (philosophy), Hecke algebra, Algebra over a field