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...

Let G be a finite group and p a prime number. The Plesken Lie algebra is a subalgebra of the complex group algebra C[G] and admits a directsum decomposition into simple Lie algebras. We describe finite-field versions of the Plesken Lie algebra via traditional and computational methods. The computations motivate our conjectures on the general structure of the modular Plesken Lie algebra.

some lie algebra analogues of schur's theorem and its converses are presented. as a result, it is shown that for a capable lie algebra l we always have dim l=z(l)  2(dim(l2))2. we also give give some examples sup- porting our results.

We associate to any germ of an analytic variety a Lie algebra of tangent vector fields, the tangent algebra. Conversely, to any Lie algebra of vector fields an analytic germ can be associated, the integral variety. The paper investigates properties of this correspondence: The set of all tangent algebras is characterized in purely Lie algebra theoretic terms. And it is shown that the tangent alg...

Let Pn = K[x1, . . . , xn] be a polynomial algebra over a field K of characteristic zero and div0n (respectively, div c n) be the Lie algebra of derivations of Pn with zero (respectively, constant) divergence. We prove that AutLie(div 0 n) ≃ AutK−alg(Pn) (n ≥ 2) and AutLie(div c n) ≃ AutK−alg(Pn). The Lie algebra div c n is a maximal Lie subalgebra of DerK(Pn). Minimal finite sets of generators...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

A C∞-Hopf algebra is a C∞-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C∞-Hopf algebras which are given by the algebra C∞(G) of smooth functions on some compact Lie group G, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

Energy-momentum tensor for the toroidal Lie algebras. Abstract. We construct vertex operator representations for the full (N + 1)-toroidal Lie algebra g. We associate with g a toroidal vertex operator algebra, which is a tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine sl N VOA and a twisted Heisenberg-Virasoro VOA. The modules for the toroidal VOA are also modules...

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.