Abelian gauge-like groups of $L_\infty$-algebras
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915737091702784 |
|---|---|
| author | Saleh, Bashar |
| author_facet | Saleh, Bashar |
| contents | Given a finite type degree-wise nilpotent $L_\infty$-algebra, we construct an abelian group that acts on the set of Maurer-Cartan elements of the given $L_\infty$-algebra so that the quotient by this action becomes the moduli space of equivalence classes of Maurer-Cartan elements. Specializing this to degree-wise nilpotent dg Lie algebras, we find that the associated ordinary gauge group of the dg Lie algebra with the Baker-Campbell-Hausdorff multiplication might be substituted by the underlying additive group. This additive group acts on the Maurer-Cartan elements, and the quotient by this action yields the moduli space of gauge-equivalence classes of Maurer-Cartan elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08512 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Abelian gauge-like groups of $L_\infty$-algebras Saleh, Bashar Rings and Algebras Algebraic Topology Quantum Algebra Given a finite type degree-wise nilpotent $L_\infty$-algebra, we construct an abelian group that acts on the set of Maurer-Cartan elements of the given $L_\infty$-algebra so that the quotient by this action becomes the moduli space of equivalence classes of Maurer-Cartan elements. Specializing this to degree-wise nilpotent dg Lie algebras, we find that the associated ordinary gauge group of the dg Lie algebra with the Baker-Campbell-Hausdorff multiplication might be substituted by the underlying additive group. This additive group acts on the Maurer-Cartan elements, and the quotient by this action yields the moduli space of gauge-equivalence classes of Maurer-Cartan elements. |
| title | Abelian gauge-like groups of $L_\infty$-algebras |
| topic | Rings and Algebras Algebraic Topology Quantum Algebra |
| url | https://arxiv.org/abs/2311.08512 |