Invariants of FP-Projective Dimensions Under Cleft Extensions
Keyword(s):
Let H be a finite dimensional Hopf algebra and A be an algebra over a fixed field k. Firstly, it is proved that the left FP-projective dimension is invariant under cleft extensions when H is semisimple and A is left coherent. Secondly, using (co)induction functors, we study the relations between FP-projective dimensions in A # H-Mod and the counterparts in AH-Mod. Finally, we characterize the FP-projective preenvelopes (resp., precovers) under H*-extensions and cleft extensions, respectively.
1971 ◽
Vol 68
(11)
◽
pp. 2631-2633
◽
1975 ◽
Vol 53
(1)
◽
pp. 9
◽
2014 ◽
Vol 14
(02)
◽
pp. 1550021
2018 ◽
Vol 168
(3)
◽
pp. 473-503
1975 ◽
Vol 53
(1)
◽
pp. 9-9
2003 ◽
Vol 2003
(26)
◽
pp. 1627-1632
1975 ◽
Vol 81
(6)
◽
pp. 1103-1106
◽
Keyword(s):