The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities.
The structure of standard modules. II. The case A1(1), principal gradation.
The Supetrace on the Grassmann envelope M(m,n;Λ)
The supports of simple modules over toroidal algebras.
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...
The tensor category of linear maps and Leibniz algebras.
The Theory and Structure of Dual JB-Algebras.
The triple-norm extension problem: the nondegenerate complete case.
We prove that, if A is an associative algebra with two commuting involutions τ and π, if A is a τ-π-tight envelope of the Jordan Triple System T:=H(A,τ) ∩ S(A,π), and if T is nondegenerate, then every complete norm on T making the triple product continuous is equivalent to the restriction to T of an algebra norm on A.
The unitary dual of G2.
The variety of dual mock-Lie algebras
We classify all complex - and -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex -dimensional dual mock-Lie algebras.
The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0
2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0. The algebras of this variety are left nilpotent of class not more than 3. We give a complete description of the vector space of multilinear identities in the language of representation theory of the symmetric group Sn and Young diagrams. We also show that the...
The variety of Lie bialgebras.
The Virasoro algebra and some exceptional Lie and finite groups.
The wedge sum of differential spaces
[For the entire collection see Zbl 0742.00067.]Differential spaces, whose theory was initiated by R. Sikorski in the sixties, provide an abstract setting for differential geometry. In this paper the author studies the wedge sum of such spaces and deduces some basic results concerning this construction.
The Wells map for abelian extensions of 3-Lie algebras
The Wells map relates automorphisms with cohomology in the setting of extensions of groups and Lie algebras. We construct the Wells map for some abelian extensions of 3-Lie algebras to obtain obstruction classes in for a pair of automorphisms in to be inducible from an automorphism of . Application to free nilpotent 3-Lie algebras is discussed.
The Yang-Baxter and pentagon equation
The -function in -algebras.
Théorème de Cohen-Hewitt dans une algèbre de Jordan-Fréchet.
Théorème de Gelfand-Mazur dans les algèbres p-normées non-associatives.
Théorèmes de factorisation dans les algèbres completes de Jordan.
A generalization of a result of Cohen-Hewitt is given in the case of Jordan-Banach algebras. Some precisions of factorization are obtained.