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The right-normed basis for a free Lie superalgebra and Lyndon-Shirshov words. (Russian, English) Zbl 1115.17003
Algebra Logika 45, No. 4, 458-483 (2006); translation in Algebra Logic 45, No. 4, 261-276 (2006).
Summary: We construct a basis for a free Lie superalgebra consisting of right-normed words $$[a_{i_1}[a_{i_2}[ \dots [a_{i_{t-1}}a_{i_t}] \dots ]]]$$, where $$a_{i_j}$$ are free generators.

##### MSC:
 17B01 Identities, free Lie (super)algebras 16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 20F12 Commutator calculus 20F14 Derived series, central series, and generalizations for groups
##### Keywords:
Lie algebra; Lyndon-Shirshov word; Lie superalgebra; basis
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