Gradings on simple Jordan and Lie algebras

DOI10.1016/j.jalgebra.2004.10.007zbMath1066.17018OpenAlexW2035841452WikidataQ115351690 ScholiaQ115351690MaRDI QIDQ1763756

Ivan Pavlovic Shestakov, Mikhail V. Zaicev, Yu. A. Bakhturin

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2004.10.007

zbMATH Keywords

involution simple classical Lie algebra Gradings simple special Jordan algebra.

Mathematics Subject Classification ID

Graded Lie (super)algebras (17B70) Graded rings and modules (associative rings and algebras) (16W50) Jordan structures associated with other structures (17C50) Super structures (17C70)

Related Items

On the structure of graded Lie algebras of order 3 ⋮ On the structure of graded 3-Leibniz algebras ⋮ Homogeneous involutions on upper triangular matrices ⋮ Gradings on Lie triple systems related to exceptional Lie algebras ⋮ GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS ⋮ Gradings on \(\mathfrak {g}_2\) ⋮ Unnamed Item ⋮ Gradings on symmetric composition algebras ⋮ Gradings on the Albert algebra and on \(\mathfrak{f}_4\) ⋮ Degree-inverting involution on full square and triangular matrices ⋮ Group gradings on the Jordan algebra of upper triangular matrices ⋮ On extended graded Poisson algebras ⋮ On the *-polynomial identities of \(M_{1,1}(E)\). ⋮ Gradings, braidings, representations, paraparticles: some open problems ⋮ On groupoid gradings ⋮ Techniques of graphs in the study of the structure of graded modules ⋮ On arbitrarily graded rings ⋮ Group gradings on the Lie and Jordan algebras of upper triangular matrices ⋮ Simple graded division algebras over the field of real numbers ⋮ Cohomolgies of Rota-Baxter operators on Lie superalgebras and some classifications on Witt superalgebras ⋮ Classification of group gradings on simple Lie algebras of types \(\mathcal A\), \(\mathcal B\), \(\mathcal C\) and \(\mathcal D\) ⋮ Fine gradings on simple classical Lie algebras ⋮ \(\mathbb{Z}\)-graded identities of the Lie algebras \(U_1\) ⋮ Lie algebras with a set grading ⋮ Fine Group Gradings of the Real Forms of sl(4,C), sp(4,C), and o(4,C) ⋮ A non-computational approach to the gradings on \(\mathfrak f_4\) ⋮ Involutions on graded matrix algebras. ⋮ Fine gradings and their Weyl groups for twisted Heisenberg Lie superalgebras ⋮ Elementary gradings on the Lie algebra \(UT_n^{(-)}\) ⋮ Orthogonal-gradings on \(H^*\)-algebras ⋮ Degree-inverting involutions on matrix algebras ⋮ Gradings on associative algebras with involution and real forms of classical simple Lie algebras ⋮ Gradings by Finite Groups of the Witt Algebra ⋮ Pauli gradings on Lie superalgebras and graded codimension growth ⋮ Group gradings on the Lie algebra of upper triangular matrices ⋮ ON THE STRUCTURE OF GRADED LIE SUPERALGEBRAS ⋮ Gradings and symmetries on Heisenberg type algebras ⋮ Irreducible modules for extended affine Lie algebras ⋮ Jordan gradings on associative algebras. ⋮ On the structure of graded Lie algebras ⋮ Fine gradings on the Lie algebra ⋮ Graded Involutions on Upper-triangular Matrix Algebras ⋮ Group Gradings onG₂ ⋮ Lie gradings on associative algebras ⋮ Group gradings on simple Lie algebras in positive characteristic ⋮ Hom-Lie algebras with a set grading ⋮ Group gradings on the Lie algebra \(\mathfrak{psl}_n\) in positive characteristic ⋮ Extended magmas and their applications ⋮ Group gradings \({\mathfrak o}(8,\mathbb C)\) ⋮ Multiloop realization of extended affine Lie algebras and Lie tori ⋮ On varieties parametrizing graded complex Lie algebras ⋮ Group gradings on superinvolution simple superalgebras. ⋮ Lie superalgebras with a set grading ⋮ On nonassociative graded-simple algebras over the field of real numbers ⋮ On the Structure of Graded Leibniz Algebras ⋮ Gradings on finite-dimensional simple Lie algebras ⋮ A retrospect of the research in nonassociative algebras in IME-USP ⋮ Casimir Elements for Some Graded Lie Algebras and Superalgebras ⋮ Graded involutions on block-triangular matrix algebras ⋮ Gradings on the real forms of the Albert algebra, of g2, and of f4 ⋮ Group gradings on finite dimensional incidence algebras ⋮ Gradings induced by nilpotent elements ⋮ Fine gradings and gradings by root systems on simple Lie algebras ⋮ Group Gradings on Finite Dimensional Lie Algebras ⋮ Group gradings on the Lie and Jordan superalgebrasQ(n)

Cites Work