论文标题
关于伯恩斯坦代数的结构和分类
On the structure and classification of Bernstein algebras
论文作者
论文摘要
我们证明，任何Bernstein代数$（a，ω）$都是与半程产品$ v \ ltimes _ {（\ cdot，\，ω）} \，k $相关的与交换式algebra $相关的k $（v，v，\ cdot）$（v，\ cdot）$（x^2）$（x^2 = 0 $ x $ x）内态$ω=ω^2 \ in {\ rm end} _k（v）$ v $满足两个兼容性条件的$。 $（1 + | i |）$ - 维伯恩斯坦代数的类型集由明确构造（使用线性代数工具）分类对象进行参数。任何Bernstein代数的自动形态组被描述为$（v， +）\ ltimes {\ rm gl} _k（v）$的典型半领型的亚组。
We prove that any Bernstein algebra $(A, ω)$ is isomorphic to a semidirect product $V \ltimes_{(\cdot, \, Ω)} \, k$ associated to a commutative algebra $(V, \cdot)$ such that $(x^2)^2 = 0$, for all $x\in A$ and an idempotent endomorphism $Ω= Ω^2 \in {\rm End}_k (V)$ of $V$ satisfying two compatibility conditions. The set of types of $(1 + |I|)$-dimensional Bernstein algebras is parametrized by an explicitely constructed (using linear algebra tools) classified object. The automorphisms group of any Bernstein algebra is described as a subgroup of the canonical semidirect product of groups $(V, +) \ltimes {\rm GL}_k (V)$.
