Classical and exceptional root systems and quantizations
type: Item
instance of: scholarly article
title: Classical and exceptional root systems and quantizations
zbMATH Open document ID: 1147.17012
author: H. L. Huru
published in: Acta Applicandae Mathematicae
publication date: 2008-09-02T00:00:00Z
review text: The author presents a method for quantizing semisimple Lie algebras. The previous work of the author [``Braided symmetric and exterior algebras and quantizations of braided Lie algebras'', Russ. Math. 52, No. 4 (2008); translation from Izv. Vyssh. Uchebn. Zaved. Mat. 2008, No. 4, 73--84 (2008)] was devoted to quantizations of the braided Lie algebra structure on a finite dimensional graded vector space \(V\) by quantizations of braided derivations on the exterior algebra of \(V^*\). Now the author finds quantizations of semisimple Lie algebras using the grading by their roots. The paper goes through all root systems, classical and exceptional.
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B75
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 5319025
zbMATH Keywords: simple graded Lie algebras
zbMATH Keywords: classical and exceptional root systems
zbMATH Keywords: quantizations
reviewed by: Victor Petrogradsky
MaRDI profile type: Publication
full work available at URL: s10440-008-9199-1
OpenAlex ID: W2081945382
cites work: Lectures on exceptional Lie groups. Ed. by Zafer Mahmud and Mamoru Mimura
cites work: Deformation of a Kac algebra by an abelian subgroup
cites work: Q3030982
cites work: Noncommutative differential geometry related to the Yang-Baxter equation.
cites work: Yang-Baxter equation and deformation of associative and Lie algebras
cites work: Associativity constraints, braidings and quantizations of modules with grading and action
cites work: Quantizations of braided derivations. I: Monoidal categories
cites work: Quantizations of braided derivations. II: Graded modules
cites work: Braided symmetric and exterior algebras and quantizations of braided Lie algebras
cites work: Solvability of Fuchsian equations depending on a parameter
cites work: Calculus and quantizations over Hopf algebras
cites work: Quantizations of differential equations.
cites work: Q4215784
cites work: Sequences of Z2⊗Z2 graded Lie algebras and superalgebras
cites work: Generalized Lie algebras
cites work: Q3764305
DOI: 10.1007/S10440-008-9199-1
description: scientific article; zbMATH DE number 5319025