Frobenius induction for algebras

被引：1

作者：

Coconet, Tiberiu ^{[1
]}

Marcus, Andrei ^{[2
]}

Todea, Constantin-Cosmin ^{[3
]}

机构：

[1] Univ Babes Bolyai, Fac Econ & Business Adm, Cluj Napoca, Romania

[2] Univ Babes Bolyai, Fac Math & Comp Sci, Str Kogalniceanu 1, Cluj Napoca 400084, Romania

[3] Tech Univ Cluj Napoca, Dept Math, Cluj Napoca, Romania

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 04期

关键词：

Augmented algebra; duality; Frobenius extension; induction; Hopf algebra; Hopf module algebra; smash product; HOPF-ALGEBRAS; EXTENSIONS; SUBALGEBRAS;

D O I：

10.1080/00927872.2016.1175614

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B -> A be a homomorphism of Hopf algebras and let C be an algebra. We consider the induction from B to A of C in two cases: when C is a B-interior algebra and when C is a B-module algebra. Our main results establish the connection between the two inductions. The inspiration comes from finite group representation theory, and some constructions work in even more general contexts.

引用

页码：1542 / 1557

页数：16

共 10 条

[1] Coconet T., 2009, MATHEMATICA, V51, P135
[2] A note on Frobenius extensions in Hopf algebras
Doi, Y
[J]. COMMUNICATIONS IN ALGEBRA, 1997, 25 (11) : 3699 - 3710
[3] Frobenius extensions of subalgebras of Hopf algebras
Fischman, D
Montgomery, S
Schneider, HJ
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (12) : 4857 - 4895
[4] Induction for interior algebras
Linckelmann, M
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 2002, 53 : 195 - 200
[5] Montgomery S., 1993, HOPF ALGEBRA THEIR A
[6] PUIG L, 1981, MATH Z, V176, P265, DOI 10.1007/BF01261873
[7] Puig L., 1999, Progress in Mathematics, V178
[8] REPRESENTATION-THEORY OF HOPF GALOIS EXTENSIONS
SCHNEIDER, HJ
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1990, 72 (1-2) : 196 - 231
[9] Reduction theorems for Clifford classes
Turull, A
[J]. JOURNAL OF GROUP THEORY, 2006, 9 (01) : 27 - 47
[10] ON MODULES INDUCED OR COINDUCED FROM HOPF SUBALGEBRAS
ULBRICH, KH
[J]. MATHEMATICA SCANDINAVICA, 1990, 67 (02) : 177 - 182

← 1 →