NCTS(South)/ NCKU Math Colloquium | |
| DATE | 2010-10-29¡@16:10-17:00 |
| PLACE | R204, 2F, NCTS, NCKU |
| SPEAKER | Jung-Miao Kuo (³¢®e§®)¡]National Chung Hsing University¡^ |
| TITLE | Hyperbolicity of central simple algebras with involution over a given extension |
| ABSTRACT | Let $F$ be a field and $(A,\sigma)$ a central simple $F$-algebra with involution. Let $\pi(t)$ be a separable polynomial over $F$. Let $F(\pi)=F[t]/(\pi(t))$. Tignol consider the question whether the algebra $A\otimes F(\pi)$ is hyperbolic. He introduced the algebra $H_\pi$, which is universal for this question. Haile and Tignol determined the structure of the algebra $H_\pi$ and introduced a certain homomorphic image $C_\pi$ of $H_\pi$. In this talk, we first present these results and then give a new characterization of $C_\pi$. We also introduce a new algebra $A_\pi$, that classifies the commutative algebras with involution that become hyperbolic over $F(\pi)$, and determine its the structure. |