A computational approach to Shephard groups

DOI10.1007/978-981-16-8422-7_16zbMath1497.20045OpenAlexW4240449612MaRDI QIDQ2089482

Dong-il Lee

Publication date: 22 October 2022

Full work available at URL: https://doi.org/10.1007/978-981-16-8422-7_16

zbMATH Keywords

Hecke algebraShephard groupGröbner-Shirshov basiscomplex reflection group

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Hecke algebras and their representations (20C08) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Computational aspects of associative rings (general theory) (16Z05) Computational methods for problems pertaining to group theory (20-08)

Cites Work

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• The cubic Hecke algebra on at most 5 strands.
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• GRÖBNER-SHIRSHOV BASES FOR COXETER GROUPS
• The BMR freeness conjecture for the 2-reflection groups
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• GRÖBNER—SHIRSHOV BASES AND NORMAL FORMS FOR THE COXETER GROUPS E₆ AND E₇
• The BMR freeness conjecture for the tetrahedral and octahedral families
• Some Algorithmic Problems for Lie Algebras
• Representations of Ariki–Koike algebras and Gröbner–Shirshov bases
• Monomial bases for the primitive complex Shephard groups of rank three
• BMR Freeness for Icosahedral Family
• Standard monomials for the Weyl group F ₄
• Regular Complex Polytopes
• Finite Unitary Reflection Groups
• Invariants of Finite Groups Generated by Reflections

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