Braided version of Shirshov-Witt theorem

DOI10.1016/j.jalgebra.2005.03.034zbMath1082.17005OpenAlexW2007616271MaRDI QIDQ2581394

Vladislav Kharchenko

Publication date: 10 January 2006

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2005.03.034

zbMATH Keywords

free Lie algebraprimitive elementsHopf algebrafree associative algebrabraided spaceShirshov-Witt theorem

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Universal enveloping (super)algebras (17B35) Identities, free Lie (super)algebras (17B01) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items

Connected braided Hopf algebras., Free braided nonassociative Hopf algebras and Sabinin \(\tau\)-algebras, Generalizations of Lie algebras, Primitive and almost primitive elements of Schreier varieties, A decomposition Theorem for pointed braided Hopf algebras, Gröbner–Shirshov bases and their calculation, Engel's theorem for generalized Lie algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the generalized Lie structure of associative algebras
• Biinvertible actions of Hopf algebras
• Die Unterringe der freien Lieschen Ringe
• Subalgebras of free colored Lie superalgebras
• Subalgebras of free Lie p-superalgebras
• The equivalence of certain categories of twisted Lie and Hopf algebras over a commutative ring
• Weak Hopf algebras and some new solutions of the quantum Yang-Baxter equation
• An existence condition for multilinear quantum operations
• A Schur double centralizer theorem for cotriangular Hopf algebras and generalized Lie algebras
• Braided Hopf algebras arising from matched pairs of groups
• Constants of coordinate differential calculi defined by Yang-Baxter operators.
• Braided Lie algebras and bicovariant differential calculi over co-quasitriangular Hopf algebras
• Hopf Galois extensions, triangular structures, and Frobenius Lie algebras in prime characteris\-tic.
• Minimal quasitriangular Hopf algebras
• Rings nonembeddable in fields with multiplicative semigroups embeddable in groups
• On a question of Mal'cev
• Baer invariants and the Birkhoff-Witt theorem
• On the immersion of an algebraic ring into a field
• The Right Braids, Quasi-braided Pre-tensor Categories, and General Yang–Baxter Operators
• Two dual classes of bialgebras related to the concepts of “quantum group” and “quantum lie algebra”
• Solutions to the Quantum Yang-Baxter Equation Arising from Pointed Bialgebras
• The Class of Rings Embeddable in Skew Fields
• A characterization of the borel-like subalgebras of quantum enveloping algebras
• On the Representation of Lie Rings in Associative Rings