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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17771 |
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Table of Contents:
- A *Gerstenhaber-Schack (G-S) bialgebra* consists of a graded Hopf algebra $H$ together with multilinear operations $\{ω^1_3,ω^2_2,ω^3_1\}\subset \{Hom^{-1}(H^{\otimes m},H^{\otimes n}): m+n=4\},$ whose sum is the degree $-1$ component of a $2$-cocycle in the G-S complex of $H$. A *G-S extension* of a graded Hopf algebra $H$ is a G-S bialgebra containing $H$. G-S extensions of $H$ are classified up to isomorphism by the degree $-1$ component of the G-S cohomology group $H_{GS}^{2}(H;H)$. We exhibit a space $X$ and a non-trivial topologically induced G-S bialgebra structure on $H^{\ast}\left( ΩX;\mathbb{Z}_{2}\right) .$