排序方式: 共有16条查询结果,搜索用时 15 毫秒
1.
Georges Pinczon 《Letters in Mathematical Physics》2007,82(2-3):237-253
We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first
one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002),
which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones).
Dedicated to my friend J.-C. Cortet. 相似文献
2.
We prove an Amitsur–Levitzki type theorem for the Lie superalgebras $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)$ ) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras $\mathfrak{g}\mathfrak{l}\left( {p,q} \right)$ cannot satisfy an Amitsur–Levitzki type super identity if pq≠0 and conjecture that neither can any other classical simple Lie superalgebra with the exception of $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left( {1,2n} \right)$ . 相似文献
3.
LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras. 相似文献
4.
Minh Thanh Duong Georges Pinczon Rosane Ushirobira 《Algebras and Representation Theory》2012,15(6):1163-1203
We define a new invariant of quadratic Lie algebras and give a complete study and classification of singular quadratic Lie algebras, i.e. those for which the invariant does not vanish. The classification is related to O(n)-adjoint orbits in $\mathfrak{o}(n)$ . 相似文献
5.
In Gerstenhaber's classical theory of deformations, the deformation parameter commutes with the original algebra. Motivated by some non classical deformations which recently appeared for quantization of Nambu mechanics, we introduce new deformations where the parameter no longer commutes with the original algebra. We find the associated cohomology and Gerstenhaber algebra and give rigidity and integrability criterions. We show that the Weyl algebra (though rigid in classical theory) can be nontrivially deformed, in super-commutative theory, to the supersymmetry enveloping algebra
相似文献
6.
We show that continuous and differential deformation theories of the algebra of smooth functions on
are the same, and that the same result holds for the algebra of formal series. We show that preferred quantizations of formal groups are always differential. 相似文献
7.
Using the duality and the topological theory of well-behaved Hopf algebras, we construct star-product models of noncompact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple Lie algebras. Our star-products act not only on coefficient functions of finite-dimensional representations, but actually on allC
functions, and they even exist for nonlinear (semi-simple) Lie groups. 相似文献
8.
We show how Lie superalgebra deformation theory can be treated by graded Lie algebras formalism. Rigidity and integrability theorems are obtained. 相似文献
9.
We introduce a natural (Fréchet-Hopf) algebra A containing all generic Jimbo algebras U
t
(sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U
t
(sl(2)). The Universal R-matrices converge in A
A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras. 相似文献
10.
In this article we study the extensions of Banach space representations of a Lie group G. We introduce different spaces of 1-cohomology on G, or on its Lie algebra , and make the connection between these spaces and the equivalence (or weak equivalence) classes of extensions.We characterize, from the properties of the 1-cohomology groups, the spaces of differentiable and analytic vectors of an extension and prove a kind of Whitehead's lemma.For Lie groups with a large compact subgroup K, we specialize to K-finite representations, and introduce and study Naimark equivalence of extensions.The results are applied to classify the extensions of the irreducible representations of . 相似文献