Remarks on Sekine quantum groups

Jialei Chen; Shilin Yang

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 3, page 695-707
  • ISSN: 0011-4642

Abstract

top
We first describe the Sekine quantum groups 𝒜 k (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of 𝒜 k and describe their representation rings r ( 𝒜 k ) . Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of r ( 𝒜 k ) .

How to cite

top

Chen, Jialei, and Yang, Shilin. "Remarks on Sekine quantum groups." Czechoslovak Mathematical Journal 72.3 (2022): 695-707. <http://eudml.org/doc/298387>.

@article{Chen2022,
abstract = {We first describe the Sekine quantum groups $\mathcal \{A\}_\{k\}$ (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of $\mathcal \{A\}_\{k\}$ and describe their representation rings $r(\mathcal \{A\}_\{k\})$. Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of $r(\mathcal \{A\}_\{k\})$.},
author = {Chen, Jialei, Yang, Shilin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sekine quantum group; representation ring; Casimir number},
language = {eng},
number = {3},
pages = {695-707},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on Sekine quantum groups},
url = {http://eudml.org/doc/298387},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Chen, Jialei
AU - Yang, Shilin
TI - Remarks on Sekine quantum groups
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 3
SP - 695
EP - 707
AB - We first describe the Sekine quantum groups $\mathcal {A}_{k}$ (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of $\mathcal {A}_{k}$ and describe their representation rings $r(\mathcal {A}_{k})$. Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of $r(\mathcal {A}_{k})$.
LA - eng
KW - Sekine quantum group; representation ring; Casimir number
UR - http://eudml.org/doc/298387
ER -

References

top
  1. Etingof, P., Ostrik, V., 10.17323/1609-4514-2004-4-3-627-654, Mosc. Math. J. 4 (2004), 627-654. (2004) Zbl1077.18005MR2119143DOI10.17323/1609-4514-2004-4-3-627-654
  2. Franz, U., Skalski, A., 10.1016/j.jalgebra.2009.05.037, J. Algebra 322 (2009), 1774-1802. (2009) Zbl1176.43005MR2543634DOI10.1016/j.jalgebra.2009.05.037
  3. Kac, G. I., Paljutkin, V. G., Finite ring groups, Trans. Mosc. Math. Soc. 15 (1966), 251-294. (1966) Zbl0218.43005MR0208401
  4. Lorenz, M., 10.1090/conm/537, Groups, Algebras and Applications Contemporary Mathematics 537. AMS, Providence (2011), 269-289. (2011) Zbl1254.16014MR2799106DOI10.1090/conm/537
  5. Sekine, Y., 10.1090/S0002-9939-96-03199-1, Proc. Am. Math. Soc. 124 (1996), 1139-1147. (1996) Zbl0845.46031MR1307564DOI10.1090/S0002-9939-96-03199-1
  6. Vaes, S., Vainerman, L., 10.1016/S0001-8708(02)00040-3, Adv. Math. 175 (2003), 1-101. (2003) Zbl1034.46068MR1970242DOI10.1016/S0001-8708(02)00040-3
  7. Wang, Z., Li, L., Zhang, Y., 10.1017/S0017089517000246, Glasg. Math. J. 60 (2018), 253-272. (2018) Zbl1444.16025MR3733845DOI10.1017/S0017089517000246
  8. Zhang, H., 10.1080/00927872.2019.1579335, Commun. Algebra 47 (2019), 4095-4113. (2019) Zbl07089356MR3975989DOI10.1080/00927872.2019.1579335

NotesEmbed ?

top

You must be logged in to post comments.