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2012 | 10 | 3 | 958-968
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Odd H-depth and H-separable extensions

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Let C n(A,B) be the relative Hochschild bar resolution groups of a subring B ⊆ A. The subring pair has right depth 2n if C n+1(A,B) is isomorphic to a direct summand of a multiple of C n(A,B) as A-B-bimodules; depth 2n + 1 if the same condition holds only as B-B-bimodules. It is then natural to ask what is defined if this same condition should hold as A-A-bimodules, the so-called H-depth 2n − 1 condition. In particular, the H-depth 1 condition coincides with A being an H-separable extension of B. In this paper the H-depth of semisimple subalgebra pairs is derived from the transpose inclusion matrix, and for QF extensions it is derived from the odd depth of the endomorphism ring extension. For general extensions characterizations of H-depth are possible using the H-equivalence generalization of Morita theory.
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Tom
10
Numer
3
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958-968
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wydano
2012-06-01
online
2012-03-24
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autor
Bibliografia
  • [1] Boltje R., Danz S., Külshammer B., On the depth of subgroups and group algebra extensions, J. Algebra, 2011, 335, 258–281 http://dx.doi.org/10.1016/j.jalgebra.2011.03.019
  • [2] Boltje R., Külshammer B., On the depth 2 condition for group algebra and Hopf algebra extensions, J. Algebra, 2010, 323(6), 1783–1796 http://dx.doi.org/10.1016/j.jalgebra.2009.11.043
  • [3] Boltje R., Külshammer B., Group algebra extensions of depth one, Algebra Number Theory, 2011, 5(1), 63–73 http://dx.doi.org/10.2140/ant.2011.5.63
  • [4] Brzezinski T., Wisbauer R., Corings and Comodules, London Math. Soc. Lecture Note Ser., 309, Cambridge University Press, 2003
  • [5] Burciu S., On some representations of the Drinfel’d double, J. Algebra, 2006, 296(2), 480–504 http://dx.doi.org/10.1016/j.jalgebra.2005.09.004
  • [6] Burciu S., Depth one extensions of semisimple algebras and Hopf subalgebras, preprint available at http://arxiv.org/abs/1103.0685
  • [7] Burciu S., Kadison L., Külshammer B., On subgroup depth, Int. Electron. J. Algebra, 2011, 9, 133–166
  • [8] Danz S., The depth of some twisted group algebra extensions, Comm. Algebra, 2011, 39(5), 1631–1645 http://dx.doi.org/10.1080/00927871003738980
  • [9] Fritzsche T., The depth of subgroups of PSL(2,q), J. Algebra, 2011, 349, 217–233 http://dx.doi.org/10.1016/j.jalgebra.2011.10.017
  • [10] Hirata K., Some types of separable extensions of rings, Nagoya Math. J., 1968, 33, 107–115
  • [11] Hirata K., Sugano K., On semisimple extensions and separable extensions over non commutative rings, J. Math. Soc. Japan, 1966, 18(4), 360–373 http://dx.doi.org/10.2969/jmsj/01840360
  • [12] Hochschild G., Relative homological algebra, Trans. Amer. Math. Soc., 1956, 82, 246–269 http://dx.doi.org/10.1090/S0002-9947-1956-0080654-0
  • [13] Kac G.I., Paljutkin V.G., Finite ring groups, Trudy Moskov. Mat. Obshch., 1966, 15, 224–261 (in Russian)
  • [14] Kadison L., New Examples of Frobenius Extensions, Univ. Lecture Ser., 14, American Mathematical Society, Providence, 1999
  • [15] Kadison L., Note on Miyashita-Ulbrich action and H-separable extension, Hokkaido Math. J., 2001, 30(3), 689–695
  • [16] Kadison L., Hopf algebroids and H-separable extensions, Proc. Amer. Math. Soc., 2003, 131(10), 2993–3002 http://dx.doi.org/10.1090/S0002-9939-02-06876-4
  • [17] Kadison L., Depth two and the Galois coring, In: Noncommutative Geometry and Representation Theory in Mathematical Physics, Karlstad, July 5–10, 2004, Contemp. Math., 391, American Mathematical Society, Providence, 2005, 149–156 http://dx.doi.org/10.1090/conm/391/07325
  • [18] Kadison L., Finite depth and Jacobson-Bourbaki correspondence, J. Pure Appl. Algebra, 2008, 212(7), 1822–1839 http://dx.doi.org/10.1016/j.jpaa.2007.11.007
  • [19] Kadison L., Infinite index subalgebras of depth two, Proc. Amer. Math. Soc., 2008, 136(5), 1523–1532 http://dx.doi.org/10.1090/S0002-9939-08-09077-1
  • [20] Kadison L., Subring depth, Frobenius extensions and their towers, unpublished manuscript
  • [21] Kadison L., Külshammer B., Depth two, normality and a trace ideal condition for Frobenius extensions, Comm. Algebra, 2006, 34(9), 3103–3122 http://dx.doi.org/10.1080/00927870600650291
  • [22] Kadison L., Szlachányi K., Bialgebroid actions on depth two extensions and duality, Adv. Math., 2003, 179(1), 75–121 http://dx.doi.org/10.1016/S0001-8708(02)00028-2
  • [23] Masuoka A., Semisimple Hopf algebras of dimension 6, 8, Israel J. Math., 1995, 92(1–3), 361–373 http://dx.doi.org/10.1007/BF02762089
  • [24] Morita K., The endomorphism ring theorem for Frobenius extensions, Math. Z., 1967, 102, 385–404 http://dx.doi.org/10.1007/BF01111076
  • [25] Müller B., Quasi-Frobenius Erweiterungen, Math. Z., 1964, 85, 345–368 http://dx.doi.org/10.1007/BF01110680
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