The resulting algebra is known as the Hall algebra HA of A. Hall algebras first appeared in the work of Steinitz [S] and Hall [H] in the case where A is the category of Abelian p-groups. They reemerged in the work of Ringel [R1]-[R3], who showed in [R1] that when A is the category of quiver representations of an A-D-E quiver ~ Q over a finite field Fq, the Hall algebra of A provides a realizati...

The complete structure of the WG2 algebra is obtained from an explicit realization by an abstract Virasoro algebra and a free boson field. We then construct its BRST operator and find a seven-parameter family of nilpotent BRST operators. These free parameters are related to the canonical transformations of the ghost, antighost fields which leave the total stress-energy tensor and the antighost ...

We study permutation orbifolds of the 2-fold and 3-fold tensor product for Virasoro vertex algebra Vc central charge c. In particular, we show that all but finitely many charges (Vc?3)Z3 is a W-algebra type (2,4,5,63,7,83,93,102). also their simple quotients obtain new realizations certain rational affine W-algebras associated to principal nilpotent element. Further analysis celebrated (2,5)-mi...

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([17]) Ando-Kirchberg ([2]). In this paper we give a complete answer to their question: A C*-algebra has algebra if only satisfies Fell's condition. contrast, show that any non-trivial extension compact operators not non-abelian but even residually type I algebra. particular its...

Let g be a complex simple Lie algebra, with fixed Borel subalgebra b⊂g and Weyl group W. Expanding on previous work of Fan Stembridge in the simply laced case, this note aims to study fully commutative elements W, their connections spherical nilpotent orbits g. If is not type G2, it shown that an element w∈W if only b determined by inversions w lies closure orbit. A similar characterization als...

The structure of a solvable Lie groups admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent algebra to be an Einstein nilradical whose Einstein derivation has simple eigenvalues. As an application, we classify filiform Einstein nilradicals (modulo known ...

Given tuples a1, . . . , ak and b in A n for some algebraic structure A, the subpower membership problem asks whether b is in the subalgebra of An that is generated by a1, . . . , ak . For A a finite group, there is a folklore algorithm which decides this problem in time polynomial in n and k. We show that the subpower membership problem for any finite Mal’cev algebra is in NP and give a polyno...

Building on the work of K. Chiba (J. Algebra 263 (2003), 75– 87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the universal field of fractions of a free associative algebra. Several applications to division rings generated by torsion-free nilpotent groups, skew Laurent se...

The commutator of Lie algebra is extended to a product of fuzzy Lie subspaces over fuzzy field. An action of fuzzy field is introduced as an extension of scalar multiplication in Lie algebra. The notion of derived series and descending central series of fuzzy Lie ∼ideal over fuzzy field and the concepts of ∼nilpotent and ∼solvable fuzzy Lie ∼ideals over fuzzy field are studied. Mathematics Subj...