본문 바로가기
KERD
논문KCI 등재

EQUIVARIANT CROSSED MODULES AND COHOMOLOGY OF GROUPS WITH OPERATORS

Nguyen Tien Quang|Pham Thi Cuc
대한수학회 (The Korean Mathematical Society)|2015.07|대한수학회보 (Bulletin of the KMS)|제52권 제4호|pp. 1077-1095

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

equivariant cohomologyΓ-crossed modulestrict graded categorical groupregular graded monoidal functorequivariant extension
주제분류수학

초록

In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.

Abstract

In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.

참고문헌 (19)

  1. J. C. Baez, "Higher dimensional algebra V: 2-groups", Theory Appl. Categ, 12, pp.423~491 (2004)
  2. R. Brown, "Covering groups of non-connected topological groups revisited", Math. Proc. Cambridge Philos. Soc, 115(1), pp.97~110 (1994)
  3. R. Brown, "crossed modules and the fundamental groupoid of a topological group", Indag. Math, 38(4), pp.296~302 (1976)
  4. M. Calvo, "Higher cohomologies of modules", Algebr. Geom. Topol, 12(1), pp.343~413 (2012)
  5. A. M. Cegarra, "Graded extensions of monoidal cate-gories", J. Algebra, 241(2), pp.620~657 (2001)
  6. A. M. Cegarra, "On graded categorical groups and equivariant group extensions", Canad. J. Math, 54(5), pp.970~997 (2002)
  7. A. M. Cegarra, "Cohomology of groups with operators", Homology Homotopy Appl, 4(1), pp.1~23 (2002)
  8. P. Dedecker, "Les foncteurs ExtΠ, H2Π et H2Π non ab´eliens", C. R. Acad. Sci. Paris, 258, pp.4891~4894 (1964)
  9. A. Fr¨ohlich, "Graded monoidal categories", Compos. Math, 28, pp.229~285 (1974)
  10. A. Grothendieck, "Cat´egories fibr´ees et d´escente, (SGA I, expos´e VI)", Lecture Notes in Math, 224, pp.145~194 (1971), Springer
  11. A. Joyal, "Braided tensor categories", Adv. Math, 82(1), pp.20~78 (1993)
  12. B. Noohi, "Group cohomology with coefficients in a crossed-module", J. Inst. Math. Jussieu, 10(2), pp.359~404 (2011)
  13. N. T. Quang, "Crossed bimodules over rings and Shukla cohomology", Math. Commun, 17(2), pp.575~598 (2012)
  14. Nguyen Tien Quang, "Crossed modules and strict Gr-categories", 대한수학회논문집, 29(1), pp.9~22 (2014), 대한수학회
  15. N. T. Quang, "Monoidal functors between (braided) Gr-categories and their applications", East-West J. Math, 13(2), pp.163~186 (2011)
  16. R. L. Taylor, "Compound group extensions I", Trans. Amer. Math. Soc, 75, pp.106~135 (1953)
  17. K.-H. Ulbrich, "Group cohomology for Picard Categories", J. Algebra, 91(2), pp.464~498 (1984)
  18. K.-H. Ulbrich, "On cohomology of graded group categories", Compos. Math. Tome, 63(3), pp.409~417 (1987)
  19. J. H. C. Whitehead, "Combinatorial homotopy II", Bull. Amer. Math. Soc, 55, pp.453~496 (1949)

관련 논문AI추천

Crossed modules and strict Gr-categoriesNguyen Thu Thuy, Nguyen Tien Quang, Pham Thi Cuc대한수학회 · 대한수학회논문집2014 · 제29권 제1호Generalized crossed modules over generalized group-groupoidsH. Fulya Akız강원경기수학회 · 한국수학논문집2024 · 제32권 제1호Crossed semimodules and cat$^{\bf 1}$-monoidsSedat Temel강원경기수학회 · 한국수학논문집2019 · 제27권 제2호Derived crossed modulesTunçar Şahan강원경기수학회 · 한국수학논문집2018 · 제26권 제3호Normality and quotient in crossed modules over groupoids and 2-groupoidsSedat Temel강원경기수학회 · 한국수학논문집2019 · 제27권 제1호On the geometry of the crossed product of groupsAhmet Sinan Cevik, Eylem Guzel Karpuz, Firat Ates대한수학회 · 대한수학회보2021 · 제58권 제5호

이 간행물의 다른 논문 (28건)

ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER Fq((x−1))Zouari Sourour, Ghorbel Rimpp. 1047-1057EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO A FOURTH-ORDER DEGENERATE PARABOLIC EQUATIONBo Liang, Meishan Wang, Ying Wangpp. 1059-1068PERMANENCE OF A TWO SPECIES DELAYED COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTINGYusen Zu, Changjin Xupp. 1069-1076NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPSMohammad Javad Sadeghifard, Mohammad Reza R. Moghaddampp. 1097-1105THE EXTENDED REAL LINE AS A JULIA SETMonireh Akbari, Maryam Rabiipp. 1107-1112
원문 보기