共查询到20条相似文献,搜索用时 46 毫秒
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Alan Koch Timothy Kohl Paul J. Truman Robert Underwood 《Journal of Pure and Applied Algebra》2019,223(5):2230-2245
Let be a finite separable extension of fields whose Galois closure has Galois group G. Greither and Pareigis use Galois descent to show that a Hopf algebra giving a Hopf–Galois structure on has the form for some group N of order . We formulate criteria for two such Hopf algebras to be isomorphic as Hopf algebras, and provide a variety of examples. In the case that the Hopf algebras in question are commutative, we also determine criteria for them to be isomorphic as K-algebras. By applying our results, we complete a detailed analysis of the distinct Hopf algebras and K-algebras that appear in the classification of Hopf–Galois structures on a cyclic extension of degree , for p an odd prime number. 相似文献
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Katrina Barron Nathan Vander Werf Jinwei Yang 《Journal of Pure and Applied Algebra》2019,223(8):3295-3317
Motivated by the study of indecomposable, nonsimple modules for a vertex operator algebra V, we study the relationship between various types of V-modules and modules for the higher level Zhu algebras for V, denoted , for , first introduced by Dong, Li, and Mason in 1998. We resolve some issues that arise in a few theorems previously presented when these algebras were first introduced, and give examples illustrating the need for certain modifications of the statements of those theorems. We establish that whether or not is isomorphic to a direct summand of affects the types of indecomposable V-modules which can be constructed by inducing from an -module, and in particular whether there are V-modules induced from -modules that were not already induced by . We give some characterizations of the V-modules that can be constructed from such inducings, in particular as regards their singular vectors. To illustrate these results, we discuss two examples of : when V is the vertex operator algebra associated to either the Heisenberg algebra or the Virasoro algebra. For these two examples, we show how the structure of in relationship to determines what types of indecomposable V-modules can be induced from a module for the level zero versus level one Zhu algebras. We construct a family of indecomposable modules for the Virasoro vertex operator algebra that are logarithmic modules and are not highest weight modules. 相似文献
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Motivated by Weyl algebra analogues of the Jacobian conjecture and the tame generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl–Hayashi algebras and tensor powers of a quantization of the first Weyl algebra which arises as a primitive factor algebra of . 相似文献
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Becky Armstrong Lisa Orloff Clark Kristin Courtney Ying-Fen Lin Kathryn McCormick Jacqui Ramagge 《Journal of Pure and Applied Algebra》2022,226(3):106853
We introduce twisted Steinberg algebras over a commutative unital ring R. These generalise Steinberg algebras and are a purely algebraic analogue of Renault's twisted groupoid C*-algebras. In particular, for each ample Hausdorff groupoid G and each locally constant 2-cocycle σ on G taking values in the units , we study the algebra consisting of locally constant compactly supported R-valued functions on G, with convolution and involution “twisted” by σ. We also introduce a “discretised” analogue of a twist Σ over a Hausdorff étale groupoid G, and we show that there is a one-to-one correspondence between locally constant 2-cocycles on G and discrete twists over G admitting a continuous global section. Given a discrete twist Σ arising from a locally constant 2-cocycle σ on an ample Hausdorff groupoid G, we construct an associated twisted Steinberg algebra , and we show that it coincides with . Given any discrete field , we prove a graded uniqueness theorem for , and under the additional hypothesis that G is effective, we prove a Cuntz–Krieger uniqueness theorem and show that simplicity of is equivalent to minimality of G. 相似文献
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《Discrete Mathematics》2022,345(9):112945
The coinvariant algebra is a quotient of the polynomial ring whose algebraic properties are governed by the combinatorics of permutations of length n. A word over the positive integers is packed if whenever appears as a letter of w, so does . We introduce a quotient of which is governed by the combinatorics of packed words. We relate our quotient to the generalized coinvariant rings of Haglund, Rhoades, and Shimozono as well as the superspace coinvariant ring. 相似文献
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《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
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Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献
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