Representations and cocycle twists of color Lie algebras

DOI10.1007/s10468-006-9027-0zbMath1125.17013arXivmath/0407165OpenAlexW1973523089WikidataQ116689626 ScholiaQ116689626MaRDI QIDQ854980

Freddy M. J. van Oystaeyen, Xiao-Wu Chen, Sergei D. Silvestrov

Publication date: 20 December 2006

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407165

zbMATH Keywords

universal enveloping algebrasfinite dimensional representationscolor Lie algebrasFCR-algebrascocycle twists

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Color Lie (super)algebras (17B75) Cohomology of Lie (super)algebras (17B56)

Related Items (19)

Generalization of superalgebras to color superalgebras and their representations ⋮ On the generalized enveloping algebra of a color Lie algebra ⋮ Filiform color Lie superalgebras ⋮ Color hom-Lie algebras, color hom-Leibniz algebras and color omni-hom-Lie algebras ⋮ \(\mathbb{Z}_2\times\mathbb{Z}_2\)-generalizations of infinite-dimensional Lie superalgebra of conformal type with complete classification of central extensions ⋮ Construction of color Lie algebras from homomorphisms of modules of Lie algebras ⋮ Z 2 × Z 2 generalizations of 𝒩=2 super Schrödinger algebras and their representations ⋮ Central Extensions and Hom-Quadratic Hom-Novikov Color Algebras ⋮ The quantum spaces of certain graded algebras related to \(\mathfrak{sl}(2, \Bbbk)\) ⋮ Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras ⋮ Z 2 × Z 2 generalizations of N=1 superconformal Galilei algebras and their representations ⋮ \(\mathbb{Z}_2 \times \mathbb{Z}_2\)-graded mechanics: the quantization ⋮ Cohomology of 3-dimensional color Lie algebras ⋮ EXAMPLES OF POINTED COLOR HOPF ALGEBRAS ⋮ Integrable deformations of nilpotent color Lie superalgebras ⋮ A classification of lowest weight irreducible modules over Z22-graded extension of osp(1|2) ⋮ Associating geometry to the Lie superalgebra 𝔰𝔩(1|1) and to the color Lie algebra 𝔰𝔩^{𝔠}₂(\Bbbk) ⋮ Classification of minimal Z2×Z2-graded Lie (super)algebras and some applications ⋮ Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians

Cites Work

• The theory of Lie superalgebras. An introduction
• Invariant algebras and completely reducible representations
• EXAMPLES OF FCR-ALGEBRAS
• Generalized Lie algebras
• Sequences of Z2⊗Z2 graded Lie algebras and superalgebras
• Quantum deformations of GL_n
• Introduction to Lie Algebras and Representation Theory
• Properties and examples of FCR-algebras
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