Bases for partially commutative Lie algebras

DOI10.1007/s10469-011-9152-7zbMath1290.17003arXiv1012.1089OpenAlexW1972385307WikidataQ115384460 ScholiaQ115384460MaRDI QIDQ694225

Evgeniĭ Nikolaevich Poroshenko

Publication date: 11 December 2012

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1089

zbMATH Keywords

defining relationsGröbner-Shirshov basispartially commutative Lie algebralinear basis

Mathematics Subject Classification ID

Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Identities, free Lie (super)algebras (17B01) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items (17)

Universal equivalence of some countably generated partially commutative structures ⋮ Mal’tsev bases for partially commutative nilpotent groups ⋮ Unnamed Item ⋮ Universal equivalence of partially commutative Lie algebras ⋮ Simple associative \(\Gamma\)-conformal algebras of finite type for a torsion-free group \(\Gamma\) ⋮ Centralizers in partially commutative Lie algebras ⋮ A study on free roots of Borcherds-Kac-Moody Lie superalgebras ⋮ Root multiplicities for Borcherds algebras and graph coloring ⋮ Universal equivalence of partially commutative metabelian Lie algebras ⋮ Algebras of Jordan brackets and generalized Poisson algebras ⋮ Gröbner–Shirshov basis method for multiple tensor products of some associative algebras ⋮ A basis for a partially commutative metabelian group ⋮ Free Lie Rota-Baxter algebras ⋮ Gröbner–Shirshov bases and their calculation ⋮ Universal enveloping Lie Rota-Baxter algebras of pre-Lie and post-Lie algebras ⋮ On Universal Equivalence of Partially Commutative Metabelian Lie Algebras ⋮ Gröbner-Shirshov Bases for Free Partially Commutative Lie Algebras

Cites Work

• Partially commutative metabelian groups: centralizers and elementary equivalence.
• Universal equivalence of partially commutative metabelian groups.
• Gröbner-Shirshov bases for Lie algebras: after A. I. Shirshov
• Selected works of A. I. Shirshov. Translated by Murray Bremner and Mikhail V. Kotchetov. Edited by Leonid A. Bokut, Victor Latyshev, Ivan Shestakov and Efim Zelmanov
• Graph algebras
• The free partially commutative Lie algebra: Bases and ranks
• The lower central series of the free partially commutative group
• Automorphisms of graph groups.
• Free partially commutative structures
• Parabolic and quasiparabolic subgroups of free partially commutative groups.
• GRÖBNER-SHIRSHOV BASES FOR COXETER GROUPS
• Free differential calculus. IV: The quotient groups of the lower central series
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