منابع مشابه
Non-degenerate graded Lie algebras with a degenerate transitive subalgebra
The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler, is analyzed. Transitive irreducible graded Lie algebras L = ∑ i∈Z Li, over algebraically closed fields of characteristic p > 2, with classical reductive component L0 are considered. We show that if a non-degenerate Lie algebra L contains a transitive degenerate subalgebra L′ such that dimL1 > 1, th...
متن کاملLie Algebras and Degenerate Affine Hecke Algebras of Type A
We construct a family of exact functors from the BGG category O of representations of the Lie algebra sln(C) to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra Hl of GLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple Hl-module can be thus obtained.
متن کاملLie Algebra Prederivations and Strongly Nilpotent Lie Algebras
We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step nilpotent Lie algebra admits a non-singular prederivation.
متن کاملLie $^*$-double derivations on Lie $C^*$-algebras
A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...
متن کاملStrongly Multiplicity Free Modules for Lie Algebras and Quantum Groups
Let U be either the universal enveloping algebra of a complex semisimple Lie algebra g or its Drinfel’d-Jimbo quantisation over the field C(z) of rational functions in the indeterminate z. We define the notion of “strongly multiplicity free” (smf) for a finite dimensional U-module V , and prove that for such modules the endomorphism algebras EndU (V ⊗r) are “generic” in the sense that they are ...
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: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09558-0