Classical BV formalism for group actions

Marco Benini; Pavel Safronov; Alexander Schenkel

doi:10.1142/S0219199721500942

Classical BV formalism for group actions

Marco Benini^*, Pavel Safronov, Alexander Schenkel

^*Corresponding author for this work

School of Mathematics

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

Abstract

We study the derived critical locus of a function f: [X/G] → A1K on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) ≃ [Z/G] is a derived quotient stack for a derived affine scheme Z, whose dg-algebra of functions is described explicitly. Our results generalize the classical BV formalism in finite dimensions from Lie algebra to group actions.

Original language	English
Article number	2150094
Journal	Communications in Contemporary Mathematics
Volume	25
Issue number	1
Early online date	18 Nov 2021
DOIs	https://doi.org/10.1142/S0219199721500942
Publication status	Published - 1 Feb 2023

Keywords / Materials (for Non-textual outputs)

BV formalism
Derived algebraic geometry
derived critical locus
quotient stack

Access to Document

10.1142/S0219199721500942

https://arxiv.org/abs/2104.14886

Cite this

@article{2ad2abcdad4042a4986707bb41034e23,

title = "Classical BV formalism for group actions",

abstract = "We study the derived critical locus of a function f: [X/G] → A1K on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) ≃ [Z/G] is a derived quotient stack for a derived affine scheme Z, whose dg-algebra of functions is described explicitly. Our results generalize the classical BV formalism in finite dimensions from Lie algebra to group actions.",

keywords = "BV formalism, Derived algebraic geometry, derived critical locus, quotient stack",

author = "Marco Benini and Pavel Safronov and Alexander Schenkel",

note = "Publisher Copyright: {\textcopyright} 2023 World Scientific Publishing Company.",

year = "2023",

month = feb,

day = "1",

doi = "10.1142/S0219199721500942",

language = "English",

volume = "25",

journal = "Communications in Contemporary Mathematics",

issn = "0219-1997",

publisher = "World Scientific",

number = "1",

}

TY - JOUR

T1 - Classical BV formalism for group actions

AU - Benini, Marco

AU - Safronov, Pavel

AU - Schenkel, Alexander

PY - 2023/2/1

Y1 - 2023/2/1

N2 - We study the derived critical locus of a function f: [X/G] → A1K on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) ≃ [Z/G] is a derived quotient stack for a derived affine scheme Z, whose dg-algebra of functions is described explicitly. Our results generalize the classical BV formalism in finite dimensions from Lie algebra to group actions.

AB - We study the derived critical locus of a function f: [X/G] → A1K on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) ≃ [Z/G] is a derived quotient stack for a derived affine scheme Z, whose dg-algebra of functions is described explicitly. Our results generalize the classical BV formalism in finite dimensions from Lie algebra to group actions.

KW - BV formalism

KW - Derived algebraic geometry

KW - derived critical locus

KW - quotient stack

UR - http://www.scopus.com/inward/record.url?scp=85120381269&partnerID=8YFLogxK

U2 - 10.1142/S0219199721500942

DO - 10.1142/S0219199721500942

M3 - Article

AN - SCOPUS:85120381269

SN - 0219-1997

VL - 25

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 1

M1 - 2150094

ER -

Classical BV formalism for group actions

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Other files and links

Fingerprint

Cite this