Classical BV formalism for group actions
| Autor: | Alexander Schenkel, Pavel Safronov, Marco Benini |
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| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Applied Mathematics General Mathematics Astrophysics::Instrumentation and Methods for Astrophysics FOS: Physical sciences Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Function (mathematics) Mathematical Physics (math-ph) Quotient stack 81Txx 14A30 18N40 Mathematics - Algebraic Geometry Group action Derived algebraic geometry High Energy Physics - Theory (hep-th) Scheme (mathematics) Affine group FOS: Mathematics Computer Science::General Literature Affine transformation Locus (mathematics) Algebraic Geometry (math.AG) Mathematical Physics Mathematics |
| ISSN: | 0219-1997 1793-6683 |
| DOI: | 10.48550/arxiv.2104.14886 |
| Popis: | We study the derived critical locus of a function $f:[X/G]\to \mathbb{A}_{\mathbb{K}}^1$ on the quotient stack of a smooth affine scheme $X$ by the action of a smooth affine group scheme $G$. It is shown that $\mathrm{dCrit}(f) \simeq [Z/G]$ 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. Comment: v3: Final version accepted for publication in Communications in Contemporary Mathematics |
| Databáze: | OpenAIRE |
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