The Koszul homology algebra of the second Veronese is generated by the lowest strand

Aldo Conca; Lukas Katthän; Victor Reiner

doi:10.1016/j.jalgebra.2018.09.013

The Koszul homology algebra of the second Veronese is generated by the lowest strand

Aldo Conca, Lukas Katthän, Victor Reiner

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We show that the Koszul homology algebra of the second Veronese subalgebra of a polynomial ring over a field of characteristic zero is generated, as an algebra, by the homology classes corresponding to the syzygies of the lowest linear strand.

Original language	English (US)
Pages (from-to)	179-189
Number of pages	11
Journal	Journal of Algebra
Volume	571
DOIs	https://doi.org/10.1016/j.jalgebra.2018.09.013
State	Published - Apr 1 2021

Bibliographical note

Funding Information:
The second author was supported by the Deutsche Forschungsgemeinschaft (DFG), grant KA 4128/2-1.

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Koszul homology
Linear group
Veronese Algebra

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10.1016/j.jalgebra.2018.09.013

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title = "The Koszul homology algebra of the second Veronese is generated by the lowest strand",

abstract = "We show that the Koszul homology algebra of the second Veronese subalgebra of a polynomial ring over a field of characteristic zero is generated, as an algebra, by the homology classes corresponding to the syzygies of the lowest linear strand.",

keywords = "Koszul homology, Linear group, Veronese Algebra",

author = "Aldo Conca and Lukas Katth{\"a}n and Victor Reiner",

note = "Funding Information: The second author was supported by the Deutsche Forschungsgemeinschaft (DFG), grant KA 4128/2-1. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

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doi = "10.1016/j.jalgebra.2018.09.013",

language = "English (US)",

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AU - Conca, Aldo

AU - Katthän, Lukas

AU - Reiner, Victor

PY - 2021/4/1

Y1 - 2021/4/1

N2 - We show that the Koszul homology algebra of the second Veronese subalgebra of a polynomial ring over a field of characteristic zero is generated, as an algebra, by the homology classes corresponding to the syzygies of the lowest linear strand.

AB - We show that the Koszul homology algebra of the second Veronese subalgebra of a polynomial ring over a field of characteristic zero is generated, as an algebra, by the homology classes corresponding to the syzygies of the lowest linear strand.

KW - Koszul homology

KW - Linear group

KW - Veronese Algebra

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

The Koszul homology algebra of the second Veronese is generated by the lowest strand

Abstract

Bibliographical note

Keywords

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