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Original Articles

The Cellularity of Twisted Doubles of Algebras with Radical Square Zero

Pages 390-403 | Received 16 Apr 2014, Published online: 19 Oct 2015

REFERENCES

  • Cao , Y. Z. ( 2003 ). On the quasi-heredity and semi-simplicity of cellular algebras . J. Algebra 267 ( 1 ): 323 – 341 .
  • Deng , B. M. , Xi , C. C. ( 1994 ). Quasi-hereditary algebras which are dual extensions of algebras . Comm. Algebra 22 ( 12 ): 4717 – 4735 .
  • Deng , B. M. , Xi , C. C. ( 1995 ). Quasi-hereditary algebras which are twisted double incidence algebras of posets . Beiträge. Algebra. Geom. 36 ( 1 ): 37 – 71 .
  • Graham , J. J. , Lehrer , G. I. ( 1996 ). Cellular algebras . Invent. Math. 123 : 1 – 34 .
  • Koenig , S. , Xi , C. C. ( 1998 ). On the structure of cellular algebras. In: Reiten, I., Smalø, S., Solberg, Ø., eds. Algebras and Modules II. Canadian Mathematical Society Conference Proceedings, Vol. 24, pp. 365–386 .
  • Koenig , S. , Xi , C. C. ( 1998 ). Strong symmetry defined by twisting modules, applied to quasi-hereditary algebras with triangular decomposition and vanishing radical cube . Commun. Math. Phys. 197 : 427 – 441 .
  • Koenig , S. , Xi , C. C. ( 1999 ). On the number of cells of a cellular algebra . Comm. Algebra 27 : 5463 – 5470 .
  • Koenig , S. , Xi , C. C. ( 2000 ). A self-injective cellular algebra is weakly symmetric . J. Algebra 228 ( 1 ): 51 – 59 .
  • Koenig , S. , Xi , C. C. ( 1999 ). Cellular algebras and quasi-hereditary algebras:a comparison . Electron. Res. Announc. Amer. Math. Soc. 5 : 71 – 75 .
  • Li , Y. B. ( 2014 ). Cellularity of a new class of diagram algebras . Comm. Algebra 42 ( 10 ): 4172 – 4181 .
  • Li , Y. B. ( 2010 ). Centres of symmetric cellular algebras . Bull. Aust. Math. Soc. 82 ( 3 ): 511 – 522 .
  • Li , Y. B. ( 2012 ). Nakayama automorphisms of Frobenius cellular algebras . Bull. Aust. Math. Soc. 86 ( 3 ): 515 – 524 .
  • Li , Y. B. , Xiao , Z. K. ( 2012 ). On cell modules of symmetric cellular algebras . Monatsh. Math. 168 ( 1 ): 49 – 64 .
  • Xi , C. C. ( 1998 ). Twisted doubles of algebras I: Deformations of algebras and the Jones index . Canad. Math. Soc. Conf. Proc. 24 : 513 – 523 .
  • Xi , C. C. ( 1994 ). Quasi-hereditary algebras with a duality . J. Reine Angew. Math. 449 : 201 – 215 .
  • Xi , C. C. ( 2000 ). On the quasi-heredity of Birman-Wenzl algebras. Adv. Math. 154: 280–298 .
  • Xi , C. C. ( 1999 ). Partition algebras are cellular . Compos. Math. 119 ( 1 ): 99 – 109 .
  • Xi , C. C. , Xiang , D. J. ( 2003 ). Cellular algebras and Cartan matrices . Linear Algebra Appl. 365 : 369 – 388 .
  • Martin , P. P. ( 1991 ). Potts Models and Related Problems in Statistical Mechanics . Singapore : World Scientific .
  • Communicated by J. Zhang

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