We study the classification problem for left-symmetric algebras with commutation Lie algebra gl(n) in characteristic 0. The problem is equivalent to the classification of étale affine representations of gl(n). Algebraic invariant theory is used to characterize those modules for the algebraic group SL(n) which belong to affine étale representations of gl(n). From the classification of these modu...

We study the quantum N = 2 super-W3 algebra using the free field realization, which is obtained from the supersymmetric Miura transformation associated with the Lie superalgebra A(2|1). We compute the full operator product expansions of the algebra explicitly. It is found that the results agree with those obtained by the OPE method. ∗Address after March 1, 1993: Institute of Physics, University...

We consider the lower central filtration of the free associative algebra An with n generators as a Lie algebra. We consider the associated graded Lie algebra. It is shown that this Lie algebra has a huge center which belongs to the cyclic words, and on the quotient Lie algebra by the center there acts the Lie algebraWn of polynomial vector fields on C. We compute the space [An, An]/[An, [An, An...

We give explicit formulas for the cohomology of the Heisenberg Lie algebras over fields of finite characteristic. We use this to show that in characteristic two, unlike all other cases, the Betti numbers are unimodal. The Heisenberg Lie algebra is the algebra hm with basis {x1, . . . , xm, y1, . . . , ym, z} and nonzero relations [xi, yi] = z, 1 ≤ i ≤ m. The cohomology (with trivial coefficient...

A current Lie algebra is contructed from a tensor product of a Lie algebra and a commutative associative algebra of dimension greater than 2. In this work we are interested in deformations of such algebras and in the problem of rigidity. In particular we prove that a current Lie algebra is rigid if it is isomorphic to a direct product g× g × ...× g where g is a rigid Lie algebra. 1 Current Lie ...

Let Sn = K[[x1, . . . , xn]] be the algebra of power series over a field K of characteristic zero, S c n be the group of continuous automorphisms of Sn with constant Jacobian, and Div c n be the Lie algebra of derivations of Sn with constant divergence. We prove that AutLie(Div c n) = AutLie,c(Div c n) ≃ S c n.

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra [1],[3],[13]. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra [13]. We also generalize the Hamitonian Lie algebra using exponential functions, and we show that these Lie algebras are simple.

In a previous paper [4] we obtained the Hopf algebra structure of k*(G ; Q(P» where G is a compact connectvd Lie group and Q(P) is the quotient ring of Z with respect to a multiplicative subset generated by a set of primes, such that H*(G ; Q(P)) is torsion free . Here we study the properties of the connective K-theory of the Lie groups Spin(n) . Since H*(Spin(n) ; Z) is torsion free if n _< 6,...