The adjoint representation of group algebras and enveloping algebras
نویسندگان
چکیده
منابع مشابه
Group Algebras and Enveloping Algebras with Nonmatrix and Semigroup Identities
Let K be a field of characteristic p > 0. Denote by ω(R) the augmentation ideal of either a group algebra R = K[G] or a restricted enveloping algebra R = u(L) over K. We first characterize those R for which ω(R) satisfies a polynomial identity not satisfied by the algebra of all 2× 2 matrices over K. Then, we examine those R for which ω(R) satisfies a semigroup identity (that is, a polynomial i...
متن کاملEnveloping Algebras of Hom-lie Algebras
A Hom-Lie algebra is a triple (L, [−,−], α), where α is a linear self-map, in which the skew-symmetric bracket satisfies an α-twisted variant of the Jacobi identity, called the Hom-Jacobi identity. When α is the identity map, the Hom-Jacobi identity reduces to the usual Jacobi identity, and L is a Lie algebra. Hom-Lie algebras and related algebras were introduced in [1] to construct deformation...
متن کاملThe Isomorphism Problem for Universal Enveloping Algebras of Lie Algebras
Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
متن کاملEnveloping Algebras and Representations of Toroidal Lie Algebras
This paper is about Toroidal Lie algebras which generalize the notion of an Affine Lie algebra. We study Verma type modules for these Toroidal algebras and prove an irreducibility criterion when the number of variables is two. We use the fact that the universal enveloping algebra is an Ore domain to obtain facts about the Verma type modules. Moreover, we are able to characterize the Affine Kac-...
متن کاملGroup identities on the units of algebraic algebras with applications to restricted enveloping algebras
An algebra A is called a GI-algebra if its group of units A satisfies a group identity. We provide positive support for the following two open problems. 1. Does every algebraic GI-algebra satisfy a polynomial identity? 2. Is every algebraically generated GI-algebra locally finite? 2000Mathematics Subject Classification. 16R40; 16R50; 16U60; 17B35.
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: Publicacions Matemàtiques
سال: 1992
ISSN: 0214-1493
DOI: 10.5565/publmat_362b92_09