[1] Zhou Nan, Wang Shuanhong,. Construction of new bornological quantum groupsbased on Galois objects [J]. Journal of Southeast University (English Edition), 2016, 32 (4): 524-526. [doi:10.3969/j.issn.1003-7985.2016.04.022]

Copy

Construction of new bornological quantum groupsbased on Galois objects()

Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

32

Issue:

2016 4

Page:

524-526

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2016-12-20

Info

Title:

Construction of new bornological quantum groupsbased on Galois objects

Author(s):

Zhou Nan;  Wang Shuanhong

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

bornological quantum groups;  actions and coactions;  Galois theory;  Galois objects

PACS:

O153.3

DOI:

10.3969/j.issn.1003-7985.2016.04.022

Abstract:

Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M(A)-module with 1x=x. There is a one-to-one corresponding relationship between the actions of A and the coactions of (^overA). If R is a Galois object for A, then there exists a faithful δ-invariant functional on R. Moreover, the Galois objects also have modular properties such as algebraic quantum groups. By constructing the comultiplication Δ, counit ε, antipode S and invariant functional φ on (^overR)⊗^(^overR), (^overR)⊗^(^overR) can be considered as a bornological quantum group.

References:

[1] van Daele A. Multiplier Hopf algebras [J]. Trans Amer Math Soc, 1994, 342(2):917-932. DOI:10.1090/s0002-9947-1994-1220906-5.
[2] van Daele A. An algebraic framework for group duality [J]. Advances in Mathematics, 1998, 140(2):323-366. DOI:10.1006/aima.1998.1775.
[3] Voigt C. Bornological quantum groups [J]. Pacific Journal of Mathematics, 2008, 235(1):93-135. DOI:10.2140/pjm.2008.235.93.
[4] van Daele A, Wang S H. Pontryagin duality for bornological quantum hypergroups [J]. Manuscripta Mathematica, 2009, 131(1):247-263. DOI:10.1007/s00229-009-0318-8.
[5] Meyer R. Smooth group representations on bornological vector spaces [J]. Bull Sci Math, 2004, 128(2):127-166. DOI:10.1016/j.bulsci.2003.12.002.
[6] Voigt C. Equivariant periodic cyclic homology [J]. Journal of the Institute of Mathematics of Jussieu, 2007, 6(4): 689-763. DOI:10.1017/s1474748007000102.
[7] de Commer K. Galois objects for algebraic quantum groups[J]. Journal of Algebra, 2009, 321(6):1746-1785. DOI:10.1016/j.jalgebra.2008.11.039.
[8] Drabant B, van Daele A, Zhang Y H. Actions of multiplier Hopf algebras [J]. Comm Algebra, 1999, 27(9):4117-4172. DOI:10.1080/00927879908826688.

Memo

Memo:

Biographies: Zhou Nan(1991—), male, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang@yahoo.com.
Citation: Zhou Nan, Wang Shuanhong.Construction of new bornological quantum groups based on Galois objects[J].Journal of Southeast University(English Edition), 2016, 32(4):524-526.DOI:10.3969/j.issn.1003-7985.2016.04.022.

Common functions