29 research outputs found
On certain vertex algebras and their modules associated with vertex algebroids
We study the family of vertex algebras associated with vertex algebroids,
constructed by Gorbounov, Malikov, and Schechtman. As the main result, we
classify all the (graded) simple modules for such vertex algebras and we show
that the equivalence classes of graded simple modules one-to-one correspond to
the equivalence classes of simple modules for the Lie algebroids associated
with the vertex algebroids. To achieve our goal, we construct and exploit a Lie
algebra from a given vertex algebroid.Comment: 32 pages. Journal of Algebra, in Pres
Classification of irreducible modules of the vertex algebra VL+ when L is a nondegenerate even lattice of an arbitrary rank
AbstractIn this paper, we first classify all irreducible modules of the vertex algebra VL+ when L is a negative definite even lattice of arbitrary rank. In particular, we show that any irreducible VL+-module is isomorphic to a submodule of an irreducible twisted VL-module. We then extend this result to a vertex algebra VL+ when L is a nondegenerate even lattice of finite rank
Rationality of the vertex algebra when is a nondegenerate even lattice of arbitrary rank
In this paper we prove that the vertex algebra is rational if is
a negative definite even lattice of finite rank, or if is a non-degenerate
even lattice of a finite rank that is neither positive definite nor negative
definite. In particular, for such even lattices , we show that the Zhu
algebras of the vertex algebras are semisimple. This extends the result
of Abe which establishes the rationality of when is a positive
definite even lattice of finite rank
Characterizations of Mersenne and 2-rooted primes
We give several characterizations of Mersenne primes (Theorem 1.1) and of
primes for which 2 is a primitive root (Theorem 1.2). These characterizations
involve group algebras, circulant matrices, binomial coefficients, and
bipartite graphs.Comment: 19 pages, final version, to appear in Finite Fields and their
Application
Leibniz Algebras and Lie Algebras
This paper concerns the algebraic structure of finite-dimensional complex
Leibniz algebras. In particular, we introduce left central and symmetric
Leibniz algebras, and study the poset of Lie subalgebras using an associative
bilinear pairing taking values in the Leibniz kernel