On Hochschild cohomology ring and integral cohomology ring for the semidihedral group

2018 ◽  
Vol 28 (02) ◽  
pp. 257-290
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Precise Description ◽  
Arbitrary Integer ◽  
Integral Cohomology ◽  
Hochschild Cohomology Ring

We will determine the ring structure of the Hochschild cohomology [Formula: see text] of the integral group ring of the semidihedral group [Formula: see text] of order [Formula: see text] for arbitrary integer [Formula: see text] by giving the precise description of the integral cohomology ring [Formula: see text] and by using a method similar to [T. Hayami, Hochschild cohomology ring of the integral group ring of the semidihedral [Formula: see text]-group, Algebra Colloq. 18 (2011) 241–258].

Hochschild Cohomology Ring of the Integral Group Ring of the Semidihedral 2-Group

2011 ◽  
Vol 18 (02) ◽  
pp. 241-258 ◽  
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Hochschild Cohomology Ring

We determine the ring structure of the Hochschild cohomology HH*(ℤ G) of the integral group ring of the semidihedral 2-group G = SD2r of order 2r.

scholarly journals Hochschild cohomology of some quantum complete intersections

2018 ◽  
Vol 17 (11) ◽  
pp. 1850215 ◽  
Author(s):  
Karin Erdmann ◽  
Magnus Hellstrøm-Finnsen
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Complete Intersections ◽  
Root Of Unity ◽  
Nilpotent Elements ◽  
Hochschild Cohomology Ring ◽  
Quantum Complete Intersections ◽  
Primitive Formula

We compute the Hochschild cohomology ring of the algebras [Formula: see text] over a field [Formula: see text] where [Formula: see text] and where [Formula: see text] is a primitive [Formula: see text]th root of unity. We find the dimension of [Formula: see text] and show that it is independent of [Formula: see text]. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.

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