A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie...

0.1. Let g be a complex finite-dimensional contragredient Lie superalgebra. These algebras were classified by V. Kac in [K1] and the list (excluding Lie algebras) consists of four series: A(m|n), B(m|n), C(m), D(m|n) and the exceptional algebrasD(2, 1, a), F (4), G(3). The finite-dimensional contragredient Lie superalgebras with zero Killing form (or, equivalently, with dual Coxeter number equa...

Rogers-Ramanujan type partition identities establish equalities between certain types of partitions with difference conditions and partitions whose generating functions is an infinite product. Since the 1980’s, many connections between representations of Lie algebras and RogersRamanujan type partition identities have emerged. Lepowsky and Wilson [6] were the first to establish this link by givi...

Abstract. This paper obtains all solvable 3-Lie algebras with the m-dimensional filiform 3-Lie algebra N (m ≥ 5) as a maximal hypo-nilpotent ideal, and proves that the m-dimensional filiform 3-Lie algebra N can’t be as the nilradical of solvable non-nilpotent 3-Lie algebras. By means of one dimensional extension of Lie algebras to the 3-Lie algebras, we get some classes of solvable Lie algebras...

We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.

Endomorphism algebras gure prominently in group representation theory. F or example, if G is a nite group of Lie type, the representation theory of the endomorphism algebra End G Cj G B |sometimes known as the Hecke algebra over C of G|plays a central role in unraveling the complex unipotent c haracters on G 22, 77. Another example arises in the modular representation theory of the nite general...

In this paper, we introduce (almost) skew 2-nomial algebras, establish the existence of a skew multiplicative K-basis for a skew 2-nomial algebra, and explore the existence of a Gröbner basis theory for such algebras. As a by-product, a family of Noetherian algebras is recognized by the finite Gröbner basis theory. Let K be a field, and let R be a finitely generated free K-algebra, or a path al...

Let B be a representation-finite C-algebra. The Z-Lie algebra L(B) associated with B has been defined by Ch. Riedtmann in [17]. If B is representation-directed there is another Z-Lie algebra associated with B defined by C. M. Ringel in [20] and denoted by K(B). We prove that the Lie algebras L(B) and K(B) are isomorphic for any representation-directed C-algebra B. 2000 Mathematics Subject Class...

we investigate the problem of the existence of a frame forright ideals of a C*-algebra A, without the use of the Kasparov stabilizationtheorem. We show that this property can not characterize A as a C*-algebraof compact operators.