Results 31 to 40 of about 104 (97)
Modular representations of Loewy length two
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 70, Page 4399-4408, 2003., 2003 Let G be a finite p‐group, K a field of characteristic p, and J the radical of the group algebra K[G]. We study modular representations using some new results of the theory of extensions of modules. More precisely, we describe the K[G]‐modules M such that J2M = 0 and give some properties and isomorphism invariants which allow us to compute the number ...
M. E. Charkani, S. Bouhamidi
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On Hopf Galois Hirata extensions
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 64, Page 4033-4039, 2003., 2003 Let H be a finite‐dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*‐Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*‐Galois Azumaya extension of BH.
George Szeto, Lianyong Xue
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The Galois algebras and the Azumay Galois extensions
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 1, Page 37-42, 2002., 2002 Let B be a Galois algebra over a commutative ring R with Galois group G, C the center of B, K = {g ∈ G | g(c) = c for all c ∈ C}, Jg{b ∈ B | bx = g(x)b for all x ∈ B} for each g ∈ K, and BK = (⊕∑g∈K Jg). Then BK is a central weakly Galois algebra with Galois group induced by K.
George Szeto, Lianyong Xue
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On certain classes of Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 5, Page 315-321, 2001., 2001 Relations between the following classes of Galois extensions are given: (1) centrally projective Galois extensions (CP‐Galois extensions), (2) faithfully Galois extensions, and (3) H‐separable Galois extensions. Moreover, it is shown that the intersection of the class of CP‐Galois extensions and the class of faithfully Galois extensions is the class ...
George Szeto, Lianyong Xue
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The closed socle of an Azumaya algebra [PDF]
Proceedings of the American Mathematical Society, 1980 If R is a Noetherian ring and A is an Azumaya algebra over R then an ideal H
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The resolution property via Azumaya algebras [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2021 Abstract Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of Azumaya algebras.
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Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Given an associative C$\mathbb {C}$‐algebra A$A$, we call A$A$ strongly rigid if for any pair of finite subgroups of its automorphism groups G,H$G, H$, such that AG≅AH$A^G\cong A^H$, then G$G$ and H$H$ must be isomorphic. In this paper, we show that a large class of filtered quantizations are strongly rigid.
Akaki Tikaradze
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On weak center Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 7, Page 489-495, 2001., 2001 Let B be a ring with 1, C the center of B, G a finite automorphism group of B, and BG the set of elements in B fixed under each element in G. Then, the notion of a center Galois extension of BG with Galois group G (i.e., C is a Galois algebra over CG with Galois group G|C≅G) is generalized to a weak center Galois extension with group G, where B is ...
George Szeto, Lianyong Xue
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Fortschritte der Physik, Volume 73, Issue 1-2, February 2025.Abstract S. Gukov and C. Vafa proposed a characterization of rational N=(1,1)$N=(1,1)$ superconformal field theories (SCFTs) in 1+1$1+1$ dimensions with Ricci‐flat Kähler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore.
Abhiram Kidambi +2 more
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