一类自入射Koszul特殊双列代数的Hochschild同调群

周俊超, 徐运阁, 陈媛

数学学报 ›› 2012, Vol. 55 ›› Issue (4) : 627-640.

PDF(568 KB)
PDF(568 KB)
数学学报 ›› 2012, Vol. 55 ›› Issue (4) : 627-640. DOI: 10.12386/A2012sxxb0059
论文

一类自入射Koszul特殊双列代数的Hochschild同调群

    周俊超, 徐运阁, 陈媛
作者信息 +

Hochschild Homology Groups of a Class of Self-Injective Koszul Special Biserial Algebras

    Jun Chao, ZHOU Yun, Ge XU, Yuan CHEN
Author information +
文章历史 +

摘要

基于Snashall与Taillefer构造的极小投射双模分解,用组合的方法,清晰地计算出一类自入射Koszul特殊双列代数ΛN的各阶Hochschild同调群的维数, 从而以计算的方式直观地表明了韩阳的猜想对这类代数ΛN成立.

Abstract

Based on the minimal projective bimodule resolution given by Snashall and Taillefer, we explicitly calculate the dimension of each Hochschild homology group of a class of self-injective Koszul special biserial algebras ΛN in terms of combinatorics, and thus show intuitively that the Han’s conjecture holds true for ΛN by means of calculation.

关键词

Hochschild同调群 / Koszul代数 / 特殊双列代数

Key words

Hochschild homology group / Koszul algebra / special biserial algebra

引用本文

导出引用
周俊超, 徐运阁, 陈媛. 一类自入射Koszul特殊双列代数的Hochschild同调群. 数学学报, 2012, 55(4): 627-640 https://doi.org/10.12386/A2012sxxb0059
Jun Chao, ZHOU Yun, Ge XU, Yuan CHEN. Hochschild Homology Groups of a Class of Self-Injective Koszul Special Biserial Algebras. Acta Mathematica Sinica, Chinese Series, 2012, 55(4): 627-640 https://doi.org/10.12386/A2012sxxb0059

参考文献

[1] Snashall N., Taillefer R., The Hochschild cohomology ring of a class of special biserial algebras, Journal ofAlgebra and Its Applications, 2010, 9(1): 73-122.
[2] Farnsteiner R., Skowrónski A., Classification of restricted Lie algebras with tame principal block, J. ReineAngew. Math., 2002, 546: 1-45.
[3] Farnsteiner R., Skowrónski A., The tame infinitesimal groups of odd characteristic, Adv. Math., 2006, 204:229-274.
[4] Erdmann K., Green E. L., Snashall N., Taillefer R., Representation theory of the Drinfeld doubles of a familyof Hopf algebras, J. Pure Appl. Algebra, 2006, 204: 413-454.
[5] Patra M. K., On the structure of nonsemisimple Hopf algebras, J. Phys. A Math. Gen., 1999, 32: 159-166.
[6] Suter R., Modules for Uq(2), Comm. Math. Phys., 1994, 163: 359-393.
[7] Xiao J., Finite-dimensional representations of Ut(2) at roots of unity, Can. J. Math., 1997, 49: 772-787.
[8] Xu Y. G., Chen Y., Hochschild homology groups of exterior algebras with two variables, Acta MathematicaSinica, Chinese Series, 2006, 49(5): 1091-1098.
[9] Buchweitz R. O., Green E. L., Madsen D., Solberg Ø., Finite Hochschild cohomology without finite globaldimension, Math. Res. Lett., 2005, 12: 805-816.
[10] Happel D., Hochschild Cohomology of Finite-Dimensional Algebras, Lecture Notes in Mathematics, Berlin:Springer, 1989, 1404: 108-126.
[11] Bergh P. A., Madsen D., Hochschild homology and global dimension, Bull. London Math. Soc., 2009, 41:473-482.
[12] Snashall N., Taillefer R., Hochschild cohomology of socle deformations of a class of Koszul self-injectivealgebras, Colloquium Mathematicum, 2010, 119: 79-93.
[13] Xu F., Hochschild and ordinary cohomology rings of small categories, Adv. Math., 2008, 219: 1872-1893.
[14] Han Y., Hochschild (co)homology dimension, J. London Math. Soc., 2006, 73: 657-668.
[15] Avramov L., Vigué-Poirrier M., Hochschild homology criteria for smoothness, Internat. Math. Res. Notices,1992, 1: 17-25.
[16] Bergh P. A., Erdmann K., Homology and cohomology of quantum complete intersections, Algebra NumberTheory, 2008, 2: 501-522.
[17] Solotar A., Vigué-Poirrier M., Two calsses of algebras with infinite Hochschild homology, Proc. Amer. Math.Soc., 2010, 138: 861-869.
[18] Bergh P. A., Han Y., Madsen D., Hochschild homology and truncated cycles, Proc. Amer. Math. Soc., 2012,140: 1133-1139.
[19] Erdmann K., Blocks of Tame Representation Type and Ralated Algebras, Lecture Notes in Mathematics,Springer, Berlin, 1990, 1428.
[20] Schröer J., On the infinite radical of a module category, Proc. London Math. Soc., 2000, 81(3): 651-674.
[21] Ringel C. M., The indecomposable repersentations of the dihedral 2-groups, Math. Ann., 1975, 214: 19-34.
[22] Gelfand I. M., Ponomarev V. A., Indecomposable representations of the Lorentz group, Russian Math.Surveys, 1068, 23: 1-58.
[23] Baues H. J., Hennes M., The homotopy classification of (n - 1)-connected (n + 3)-dimensional polyhedra,n ≥ 4, Topology, 1991, 30: 373-408.
[24] Drozd Yu. A., Greuel G. M., Tame and wild projective curves and classification of vector bundles, J. Algebra,2001, 246: 1-54.
[25] Erdmann K., Schroll S., On the Hochschild cohomology of tame Hecke algebras, Arch. Math., 2010, 94:117-127.
[26] Xu Y. G., Hochschild cohomology of special biserial algebras, Science in China, Series A, 2007, 50(8):1117-1128.
[27] Xu Y. G., On the first Hochschild cohomology of trivial extensions of special biserial algebras, Science inChina, Series A, 2004, 47(4): 578-592.

基金

国家自然科学基金(10971206, 11171325)与湖北省教育厅重点基金(D20101003)资助项目
PDF(568 KB)

Accesses

Citation

Detail

段落导航
相关文章

/