Displaying similar documents to “Remarks on algebras having two bases of different cardinalities”

Universal Enveloping Algebras of Nonassociative Structures

Tvalavadze, Marina (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 17D15. Secondary 17D05, 17B35, 17A99. This is a survey paper to summarize the latest results on the universal enveloping algebras of Malcev algebras, triple systems and Leibniz n-ary algebras.

A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems

Iván Ezequiel Angiono (2015)

Journal of the European Mathematical Society

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We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko’s theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.

Multipliers of topological algebras

Taqdir Husain

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CONTENTS1. Introduction.............................................................................................52. Multipliers of topological algebras...........................................................63. Multipliers of topological algebras with orthogonal bases......................114. π-Algebras............................................................................................185. Orthogonal decomposition of topological algebras................................216....