منابع مشابه
Central Simple Poisson Algebras
In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
متن کاملGraded Poisson Algebras
1.1. Graded vector spaces. By a Z-graded vector space (or simply, graded vector space) we mean a direct sum A = ⊕i∈ZAi of vector spaces over a field k of characteristic zero. The Ai are called the components of A of degree i and the degree of a homogeneous element a ∈ A is denoted by |a|. We also denote by A[n] the graded vector space with degree shifted by n, namely, A[n] = ⊕i∈Z(A[n])i with (A...
متن کاملNon-associative algebras associated to Poisson algebras
Poisson algebras are usually defined as structures with two operations, a commutative associative one and an anti-commutative one that satisfies the Jacobi identity. These operations are tied up by a distributive law, the Leibniz rule. We present Poisson algebras as algebras with one operation, which enables us to study them as part of non-associative algebras. We study the algebraic and cohomo...
متن کاملVertex algebras and vertex poisson algebras
This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex poisson algebra are revisited and certain general construction theorems of vertex poisson algebras are given. A notion of filtered vertex algebra is formulated in terms of a notion of good filtration and it i...
متن کاملGeneralized Witt Algebras and Generalized Poisson Algebras
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.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2007
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-04008-1