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Automorphism group of representation ring of the weak Hopf algebra H 8 ˜

Dong Su; Shilin Yang

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 4, page 1131-1148
  • ISSN: 0011-4642

Abstract

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Let H 8 be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra H 8 ˜ based on H 8 , then we investigate the structure of the representation ring of H 8 ˜ . Finally, we prove that the automorphism group of r ( H 8 ˜ ) is just isomorphic to D 6 , where D 6 is the dihedral group with order 12.

How to cite

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Su, Dong, and Yang, Shilin. "Automorphism group of representation ring of the weak Hopf algebra $\widetilde{H_8}$." Czechoslovak Mathematical Journal 68.4 (2018): 1131-1148. <http://eudml.org/doc/294302>.

@article{Su2018,
abstract = {Let $H_8$ be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra $\widetilde\{H_8\}$ based on $H_8$, then we investigate the structure of the representation ring of $\widetilde\{H_8\}$. Finally, we prove that the automorphism group of $r(\widetilde\{H_8\})$ is just isomorphic to $D_6$, where $D_6$ is the dihedral group with order 12.},
author = {Su, Dong, Yang, Shilin},
journal = {Czechoslovak Mathematical Journal},
keywords = {automorphism group; representation ring; weak Hopf algebra},
language = {eng},
number = {4},
pages = {1131-1148},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Automorphism group of representation ring of the weak Hopf algebra $\widetilde\{H_8\}$},
url = {http://eudml.org/doc/294302},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Su, Dong
AU - Yang, Shilin
TI - Automorphism group of representation ring of the weak Hopf algebra $\widetilde{H_8}$
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 1131
EP - 1148
AB - Let $H_8$ be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra $\widetilde{H_8}$ based on $H_8$, then we investigate the structure of the representation ring of $\widetilde{H_8}$. Finally, we prove that the automorphism group of $r(\widetilde{H_8})$ is just isomorphic to $D_6$, where $D_6$ is the dihedral group with order 12.
LA - eng
KW - automorphism group; representation ring; weak Hopf algebra
UR - http://eudml.org/doc/294302
ER -

References

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  1. Aizawa, N., Isaac, P. S., 10.1063/1.1616999, J. Math. Phys. 44 (2003), 5250-5267. (2003) Zbl1063.16041MR2014859DOI10.1063/1.1616999
  2. Alperin, R. C., 10.1016/0022-4049(79)90027-6, J. Pure Appl. Algebra 15 (1979), 109-115. (1979) Zbl0415.13006MR0535179DOI10.1016/0022-4049(79)90027-6
  3. Chen, H.-X., 10.1016/j.jpaa.2013.01.013, J. Pure Appl. Algebra 217 (2013), 1870-1887. (2013) Zbl1292.16021MR3053522DOI10.1016/j.jpaa.2013.01.013
  4. Chen, H., Oystaeyen, F. Van, Zhang, Y., 10.1090/S0002-9939-2013-11823-X, Proc. Am. Math. Soc. 142 (2014), 765-775. (2014) Zbl1309.16021MR3148512DOI10.1090/S0002-9939-2013-11823-X
  5. Cheng, D., The structure of weak quantum groups corresponding to Sweedler algebra, JP J. Algebra Number Theory Appl. 16 (2010), 89-99. (2010) Zbl1217.16028MR2662950
  6. Cheng, D., Li, F., 10.1080/00927870802243499, Commun. Algebra 37 (2009), 729-742. (2009) Zbl1166.16018MR2503175DOI10.1080/00927870802243499
  7. Dicks, W., 10.5565/publmat_27183_04, Publ. Secc. Mat. Univ. Autòn. Barc. 27 (1983), 155-162. (1983) Zbl0593.13005MR0763864DOI10.5565/publmat_27183_04
  8. Drensky, V., Yu, J.-T., 10.1016/j.jalgebra.2008.08.026, J. Algebra 321 (2009), 292-302. (2009) Zbl1157.13015MR2469362DOI10.1016/j.jalgebra.2008.08.026
  9. Han, J., Su, Y., Automorphism groups of Witt algebras, Available at ArXiv 1502.0144v1 [math.QA]. 
  10. Jia, T., Zhao, R., Li, L., 10.1007/s11464-016-0565-4, Front. Math. China 11 (2016), 921-932. (2016) Zbl1372.16038MR3531037DOI10.1007/s11464-016-0565-4
  11. Li, F., 10.1006/jabr.1998.7491, J. Algebra 208 (1998), 72-100. (1998) Zbl0916.16020MR1643979DOI10.1006/jabr.1998.7491
  12. Li, L., Zhang, Y., 10.1090/conm/585/11618, Hopf Algebras and Tensor Categories Contemporary Mathematics 585, Proc. of the International Conf., University of Almería, Almería, Amer. Math. Soc., Providence N. Andruskiewitsch et al. (2013), 275-288. (2013) Zbl1309.19001MR3077243DOI10.1090/conm/585/11618
  13. Masuoka, A., 10.1007/BF02762089, Isr. J. Math. 92 (1995), 361-373. (1995) Zbl0839.16036MR1357764DOI10.1007/BF02762089
  14. Montgomery, S., 10.1090/cbms/082, Conference on Hopf algebras and Their Actions on Rings, Chicago, 1992, CBMS Regional Conference Series in Mathematics 82, AMS, Providence (1993). (1993) Zbl0793.16029MR1243637DOI10.1090/cbms/082
  15. Ştefan, D., 10.1006/jabr.1998.7602, J. Algebra 211 (1999), 343-361. (1999) Zbl0918.16031MR1656583DOI10.1006/jabr.1998.7602
  16. Sweedler, M. E., Hopf Algebras, Mathematics Lecture Note Series, W. A. Benjamin, New York (1969). (1969) Zbl0194.32901MR0252485
  17. Kulk, W. van der, On polynomial rings in two variables, Nieuw Arch. Wiskd., III. Ser. 1 (1953), 33-41. (1953) Zbl0050.26002MR0054574
  18. Yang, S., 10.1142/S021949880400071X, J. Algebra Appl. 3 (2004), 91-104. (2004) Zbl1080.16043MR2047638DOI10.1142/S021949880400071X
  19. Yang, S., 10.1063/1.1933063, J. Math. Phys. 46 (2005), 073502, 18 pages. (2005) Zbl1110.16047MR2153558DOI10.1063/1.1933063
  20. Yu, J.-T., Recognizing automorphisms of polynomial algebras, Mat. Contemp. 14 (1998), 215-225. (1998) Zbl0930.13016MR1663646
  21. Zhao, K., Automophisms of the binary polynomial algebras on integer rings, Chinese Ann. Math. Ser. A 4 (1995), 448-494 Chinese. (1995) 

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