Pertinency of Hopf actions and quotient categories of Cohen–Macaulay algebras

We study invariants and quotient categories of fixed subrings of Artin-Schelter regular algebras under Hopf algebra actions.

[1]  James J. Zhang,et al.  McKay correspondence for semisimple Hopf actions on regular graded algebras, II , 2016, Journal of Noncommutative Geometry.

[2]  J. J. Zhang,et al.  Noncommutative Auslander theorem , 2016, Transactions of the American Mathematical Society.

[3]  Saul-Paul Sirag.  The McKay Correspondence , 2016 .

[4]  W. Gruyter.  Quantum binary polyhedral groups and their actions on quantum planes , 2016 .

[5]  Y. Zhang,et al.  Hopf dense Galois extensions with applications , 2015, 1512.07439.

[6]  I. Mori,et al.  Ample Group Action on AS-regular Algebras and Noncommutative Graded Isolated Singularities , 2014, 1404.5045.

[7]  C. Negron.  Spectral Sequences for the Cohomology Rings of a Smash Product , 2014, 1401.3551.

[8]  Manuel Reyes,et al.  Skew Calabi–Yau algebras and homological identities , 2013, 1302.0437.

[9]  Michel Van den Bergh,et al.  Noncommutative quadric surfaces , 2013 .

[10]  Izuru Mori,et al.  McKay‐type correspondence for AS‐regular algebras , 2013, J. Lond. Math. Soc..

[11]  Kenta Ueyama.  Graded maximal Cohen–Macaulay modules over noncommutative graded Gorenstein isolated singularities , 2013 .

[12]  James J. Zhang,et al.  Invariants of (-1)-Skew Polynomial Rings under Permutation Representations , 2013, 1305.3973.

[13]  James J. Zhang,et al.  Noncommutative Complete Intersections , 2013, 1302.6209.

[14]  K. Ajitabha,et al.  Injective resolutions of some regular rings , 2012 .

[15]  Graham J. Leuschke.  Non-Commutative Crepant Resolutions: Scenes from Categorical Geometry , 2011, 1103.5380.

[16]  I. Mori,et al.  The structure of AS-Gorenstein algebras , 2011 .

[17]  Osamu Iyama,et al.  Tilting and cluster tilting for quotient singularities , 2010, 1012.5954.

[18]  Ji-wei He,et al.  HOPF ALGEBRA ACTIONS ON DIFFERENTIAL GRADED ALGEBRAS AND APPLICATIONS , 2010, 1007.4983.

[19]  Ellen Kirkman,et al.  Gorenstein subrings of invariants under Hopf algebra actions , 2009 .

[20]  J. Guo,et al.  Selfinjective Koszul algebras of finite complexity , 2009 .

[21]  Q.-S. Wu,et al.  Koszul differential graded algebras and BGG correspondence II , 2009 .

[22]  Q.-S. Wu,et al.  KOSZUL DIFFERENTIAL GRADED ALGEBRAS AND BGG CORRESPONDENCE , 2007, 0712.1324.

[23]  D. Chan.  McKay correspondence for canonical orders , 2007, 0707.3481.

[24]  U. Washington,et al.  Rigidity of graded regular algebras , 2007, 0706.0662.

[25]  S. Skryabin,et al.  The Goldie Theorem for H-semiprime algebras , 2006 .

[26]  D. Orlov,et al.  Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities , 2005, math/0503632.

[27]  Peter Jørgensen.  A noncommutative BGG correspondence , 2005 .

[28]  I. Mori.  Riemann¿Roch like theorem for triangulated categories , 2004 .

[29]  Peter Jørgensen.  Linear free resolutions over non-commutative algebras , 2003, Compositio Mathematica.

[30]  R. Warfield,et al.  An Introduction to Noncommutative Noetherian Rings , 1989 .

[31]  C. Weibel,et al.  An Introduction to Homological Algebra: References , 1960 .

[32]  J. McConnell,et al.  Noncommutative Noetherian Rings , 2001 .

[33]  Apostolos Beligiannis.  The homological theory of contravariantly finite subcategories:auslander-buchweitz contexts, gorenstein categories and (co-)stabilization , 2000 .

[34]  R. Martínez-Villa.  Graded, Selfinjective, and Koszul Algebras , 1999 .

[35]  James J. Zhang,et al.  Rings with Auslander Dualizing Complexes , 1998, math/9804005.

[36]  K. Ajitabh,et al.  Auslander-gorenstein rings , 1998 .

[37]  James J. Zhang.  Connected Graded Gorenstein Algebras with Enough Normal Elements , 1997 .

[38]  James J. Zhang,et al.  Growth of graded noetherian rings , 1997 .

[39]  M. Reid.  McKay correspondence , 1997, alg-geom/9702016.

[40]  J. Carlson.  The decomposition of the trivial module in the complexity quotient category , 1996 .

[41]  Wolfgang Soergel,et al.  Koszul Duality Patterns in Representation Theory , 1996 .

[42]  D. Ştefan.  Hochschild cohomology on Hopf Galois extensions , 1995 .

[43]  James J. Zhang,et al.  Noncommutative Projective Schemes , 1994 .

[44]  J. T. Stafford,et al.  Homological Properties of (Graded) Noetherian PI Rings , 1994 .

[45]  W. W. Wheeler,et al.  Complexity and qoutient categories for group algebras , 1994 .

[46]  I. Reiten,et al.  k-Gorenstein algebras and syzygy modules , 1994 .

[47]  Susan Montgomery,et al.  Hopf algebras and their actions on rings , 1993 .

[48]  I. V. Verbovskii.  Integrals in Hopf algebras , 1992 .

[49]  M. Bergh,et al.  Modules over regular algebras of dimension 3 , 1991 .

[50]  Jun-ichi Miyachi,et al.  Localization of triangulated categories and derived categories , 1991 .

[51]  C. R. Hajarnavis.  AN INTRODUCTION TO NONCOMMUTATIVE NOETHERIAN RINGS , 1991 .

[52]  Davida Fischman,et al.  Irreducible actions and faithful actions of hopf algebras , 1990 .

[53]  Y. Yoshino,et al.  Cohen-Macaulay modules over Cohen-Macaulay rings , 1990 .

[54]  Maurice Auslander,et al.  Rational singularities and almost split sequences , 1986 .

[55]  Günter Krause,et al.  Growth of Algebras and Gelfand-Kirillov Dimension , 1985 .

[56]  J. Rotman.  An Introduction to Homological Algebra , 1979 .

[57]  I. Gel'fand,et al.  Algebraic bundles over Pn and problems of linear algebra , 1978 .

[58]  S. Kleiman,et al.  On the purity of the branch locus , 1971 .

[59]  M. Auslander.  On the purity of branch locus , 1962 .