Gerstenhaber-Schack Bialgebras
| Autor: | Umble, Ronald |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A *Gerstenhaber-Schack (G-S) bialgebra* consists of a graded Hopf algebra $H$ together with multilinear operations $\{\omega^1_3,\omega^2_2,\omega^3_1\}\subset \{Hom^{-1}(H^{\otimes m},H^{\otimes n}): m+n=4\},$ 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 $H^{\ast}\left( \Omega X;\mathbb{Z}_{2}\right) .$ Comment: 14 pages; 3 figures. This version removes some unnecessary content, condenses the format, and replaces symbols such as $KK_{n,m}$ with $KK^n_m$. There are numerous corrections, expositional clarifications, and a new Figure 3 |
| Databáze: | arXiv |
| Externí odkaz: |
|