Faithful representations of Leibniz algebras
نویسندگان
چکیده
منابع مشابه
Conformal Representations of Leibniz Algebras
In this note we present a more detailed and explicit exposition of the definition of a conformal representation of a Leibniz algebra. Recall (arXiv:math/0611501v3) that Leibniz algebras are exactly Lie dialgebras. The idea is based on the general fact that every dialgebra that belongs to a variety Var can be embedded into a conformal algebra of the same variety. In particular, we prove that an ...
متن کاملMinimal Faithful Representations of Reductive Lie Algebras
We prove an explicit formula for the invariant μ(g) for finite-dimensional semisimple, and reductive Lie algebras g over C. Here μ(g) is the minimal dimension of a faithful linear representation of g. The result can be used to study Dynkin’s classification of maximal reductive subalgebras of semisimple Lie algebras.
متن کاملFaithful Representations of Minimal Dimension of Current Heisenberg Lie Algebras
Given a Lie algebra g over a field of characteristic zero k, let μ(g) = min{dimπ : π is a faithful representation of g}. Let hm be the Heisenberg Lie algebra of dimension 2m + 1 over k and let k[t] be the polynomial algebra in one variable. Given m ∈ N and p ∈ k[t], let hm,p = hm ⊗ k[t]/(p) be the current Lie algebra associated to hm and k[t]/(p), where (p) is the principal ideal in k[t] genera...
متن کاملLeibniz 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.
متن کاملOn Restricted Leibniz Algebras
In this paper we prove that in prime characteristic there is a functor −p-Leib from the category of diassociative algebras to the category of restricted Leibniz algebras, generalizing the functor from associative algebras to restricted Lie algebras. Moreover we define the notion of restricted universal enveloping diassociative algebra Udp(g) of a restricted Leibniz algebra g and we show that Ud...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11788-0