Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type 𝐀 1

Bo Hou; Yanhong Guo

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 4, page 1085-1099
  • ISSN: 0011-4642

Abstract

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The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let Λ t be the Yoneda algebra of a reconstruction algebra of type 𝐀 1 over a field . I n t h i s p a p e r , a m i n i m a l p r o j e c t i v e b i m o d u l e r e s o l u t i o n o f t i s c o n s t r u c t e d , a n d t h e -dimensions of all Hochschild homology and cohomology groups of Λ t are calculated explicitly.

How to cite

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Hou, Bo, and Guo, Yanhong. "Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type ${\mathbf {A}}_{1}$." Czechoslovak Mathematical Journal 65.4 (2015): 1085-1099. <http://eudml.org/doc/276102>.

@article{Hou2015,
abstract = {The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let $\Lambda _\{t\}$ be the Yoneda algebra of a reconstruction algebra of type $\{\mathbf \{A\}\}_\{1\}$ over a field $. In this paper, a minimal projective bimodule resolution of $t$ is constructed, and the $-dimensions of all Hochschild homology and cohomology groups of $\Lambda _\{t\}$ are calculated explicitly.},
author = {Hou, Bo, Guo, Yanhong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hochschild cohomology; reconstruction algebra; Yoneda algebra},
language = {eng},
number = {4},
pages = {1085-1099},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type $\{\mathbf \{A\}\}_\{1\}$},
url = {http://eudml.org/doc/276102},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Hou, Bo
AU - Guo, Yanhong
TI - Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type ${\mathbf {A}}_{1}$
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 1085
EP - 1099
AB - The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let $\Lambda _{t}$ be the Yoneda algebra of a reconstruction algebra of type ${\mathbf {A}}_{1}$ over a field $. In this paper, a minimal projective bimodule resolution of $t$ is constructed, and the $-dimensions of all Hochschild homology and cohomology groups of $\Lambda _{t}$ are calculated explicitly.
LA - eng
KW - Hochschild cohomology; reconstruction algebra; Yoneda algebra
UR - http://eudml.org/doc/276102
ER -

References

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