共查询到20条相似文献,搜索用时 0 毫秒
1.
《Journal of Pure and Applied Algebra》2022,226(12):107130
Deformed preprojective algebras are generalizations of the usual preprojective algebras introduced by Crawley-Boevey and Holland, which have applications to Kleinian singularities, the Deligne-Simpson problem, integrable systems and noncommutative geometry. In this paper we offer three contributions to the study of such algebras: (1) the 2-Calabi-Yau property; (2) the unification of the reflection functors of Crawley-Boevey and Holland with reflection functors for the usual preprojective algebras; and (3) the classification of tilting ideals in 2-Calabi-Yau algebras, and especially in deformed preprojective algebras for extended Dynkin quivers. 相似文献
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Haisheng LI 《Frontiers of Mathematics in China》2011,6(4):707-730
We associate quantum vertex algebras and their ϕ-coordinated quasi modules to certain deformed Heisenberg algebras. 相似文献
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We study the connections between one-sided Hopf algebras and one-sided quantum quasigroups, tracking the four possible invertibility conditions for the left and right composite morphisms that combine comultiplications and multiplications in these structures. The genuinely one-sided structures exhibit precisely two of the invertibilities, while it emerges that imposing one more condition often entails the validity of all four. A main result shows that under appropriate conditions, just one of the invertibility conditions is su?cient for the existence of a one-sided antipode. In the left Hopf algebra which is a variant of the quantum special linear group of two-dimensional matrices, it is shown explicitly that the right composite is not injective, and the left composite is not surjective. 相似文献
5.
Geometry of the Moment Map for Representations of Quivers 总被引:3,自引:0,他引:3
William Crawley-Boevey 《Compositio Mathematica》2001,126(3):257-293
We study the moment map associated to the cotangent bundle of the space of representations of a quiver, determining when it is flat, and giving a stratification of its Marsden–Weinstein reductions. In order to do this we determine the possible dimension vectors of simple representations of deformed preprojective algebras. In an appendix we use deformed preprojective algebras to give a simple proof of much of Kac's Theorem on representations of quivers in characteristic zero. 相似文献
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Nanhua Xi 《Journal of the American Mathematical Society》2007,20(1):211-217
In this paper we show that the Deligne-Langlands-Lusztig classification of simple representations of an affine Hecke algebra remains valid if the parameter is not a root of the corresponding Poincaré polynomial. This verifies a conjecture of Lusztig proposed in 1989.
8.
《Journal of Pure and Applied Algebra》2023,227(1):107146
For a commutative ring R and an ADE Dynkin quiver Q, we prove that the multiplicative preprojective algebra of Crawley-Boevey and Shaw, with parameter , is isomorphic to the (additive) preprojective algebra as R-algebras if and only if the bad primes for Q – 2 in type D, 2 and 3 for , and 2, 3 and 5 for – are invertible in R. We construct an explicit isomorphism over in type D, over for , and over for . Conversely, if some bad prime is not invertible in R, we show that the additive and multiplicative preprojective algebras differ in zeroth Hochschild homology, and hence are not isomorphic. In fact, one only needs the vanishing of certain classes in zeroth Hochschild homology of the multiplicative preprojective algebra, utilizing a rigidification argument for isomorphisms that may be of independent interest.In the setting of Ginzburg dg-algebras, our obstructions are new in type E and give a more elementary proof of the negative result of Etgü–Lekili [5, Theorem 13] in type D. Moreover, the zeroth Hochschild homology of the multiplicative preprojective algebra, computed in Section 4, can be interpreted as the space of unobstructed deformations of the multiplicative Ginzburg dg-algebra by Van den Bergh duality. Finally, we observe that the multiplicative preprojective algebra is not symmetric Frobenius if , a departure from the additive preprojective algebra in characteristic 2 for , and , . 相似文献
9.
The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A
construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving
explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed
by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist
algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well
as complex reflection groups.
Received: July 25, 2001 相似文献
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In this paper, we define a class of extended quantum enveloping algebras U q (f(K, J)) and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and noncocommutative Hopf algebras. 相似文献
12.
S. E. Klevtsov 《Theoretical and Mathematical Physics》2008,154(2):201-208
We describe a construction of the quantum-deformed affine algebras using vertex operators in the free field theory. We prove
the Serre relations for the Borel subalgebras of quantum affine algebras; in particular, we consider the
case in detail. We also construct the generators corresponding to the positive roots of
.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 240–248, February, 2008. 相似文献
13.
Takehiko Yamanouchi 《Transactions of the American Mathematical Society》2003,355(7):2813-2828
It is shown that, for a minimal and integrable action of a locally compact quantum group on a factor, the group of automorphisms of the factor leaving the fixed-point algebra pointwise invariant is identified with the intrinsic group of the dual quantum group. It is proven also that, for such an action, the regularity of the fixed-point algebra is equivalent to the cocommutativity of the quantum group.
14.
Quantum Yang-Baxter module algebras 总被引:10,自引:0,他引:10
LetH be a quantum group over a commutative ringR. We introduce the concept of quantum Yang-BaxterH-module algebra, generalizing the notion ofH-dimodule algebra in the case whereH is commutative, cocommutative and faithfully projective. After discussing some examples, we introduceH-Azumaya algebras. The set of quivalence classes ofH-Azumaya algebras can be made into a group, called the Brauer group of the quantum groupH. This group is a generalization of the Brauer-Long group.This author wishes to thank the Department of Mathematics, UIA, for its hospitality and financial support during the time when most of this paper was written. 相似文献
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We study the representations of the restricted two-parameter quantum groups of types B and G . For these restricted two-parameter quantum groups, we give some explicit conditions which guarantee that a simple module can be factored as the tensor product of a one-dimensional module with a module that is naturally a module for the quotient by central group-like elements. That is, given θ a primitive l th root of unity, the factorization of simple ? θ y , θ z , ( ) - modules is possible, if and only if (2(y - z ), l ) = 1 for = ? ? 2 n + 1 ; (3(y - z ), l ) = 1 for g= G 2. 相似文献
17.
Karl-Hermann Neeb 《Semigroup Forum》2008,77(1):5-35
A host algebra of a topological group G is a C
*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite dimensional Lie groups which is based on complex involutive
semigroups. Any locally bounded absolute value α on such a semigroup S leads in a natural way to a C
*-algebra C
*(S,α), and we describe a setting which permits us to conclude that this C
*-algebra is a host algebra for a Lie group G. We further explain how to attach to any such host algebra an invariant weak-*-closed convex set in the dual of the Lie algebra
of G enjoying certain nice convex geometric properties. If G is the additive group of a locally convex space, we describe all host algebras arising this way. The general non-commutative
case is left for the future.
To K.H. Hofmann on the occasion of his 75th birthday 相似文献
18.
FAN Yun & ZHU Ping School of Mathematics Statistics Central China Normal University Wuhan China School of Mathematical Science Nankai University Tianjin China 《中国科学A辑(英文版)》2005,48(5):577-582
Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p'-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p'-subgroup is obtained. 相似文献
19.
We study actions of compact quantum groups on type I-factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz?s results concerning Peter-Weyl theory for compact quantum groups. The main new phenomenon is that for general compact quantum groups (more precisely, those which are not of Kac type), not all irreducible projective representations have to be finite-dimensional. As applications, we consider the theory of projective representations for the compact quantum groups associated with group von Neumann algebras of discrete groups, and consider a certain non-trivial projective representation for quantum SU(2). 相似文献
20.
Ming DING 《Frontiers of Mathematics in China》2011,6(2):231-240
We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When Q is a quiver of finite type, we prove that the algebra (Q) generated by all cluster characters is exactly the quantum cluster algebra (Q). 相似文献