Study of a Z-form of the coordinate ring of a reductive group

2007/09/09 by Lusztig, G. · 4 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0709.1286

Abstract

We show how the theory of canonical bases in modified universal enveloping algebras can be used to develop the theory of Chevalley groups over any commutative ring with 1.

Cited by

• Integral cluster structures on quantized coordinate rings
• Notes on Chevalley Groups and Root Category II: Compact Lie Groups and Representations
• Symmetric subgroup schemes
• A triangular decomposition for the crystal lattice of quantized function algebras

Related

• Coordinate rings on symmetric spaces
• Cluster algebras I: Foundations
• On the construction of semisimple Lie algebras and Chevalley groups
• Canonical bases and quantum coordinate ring
• The Diophantine problem in Chevalley groups