Multiplicative Complexity of Commutative Group Algebras over Algebraically Closed Fields
نویسنده
چکیده
We determine structure and multiplicative complexity of commutative group algebras over algebraically closed fields. Commutative group algebra A of dimension n over algebraically closed field is isomorphic to B, where B is a superbasic algebra of minimal rank (see [5] for definition), and t is maximal that t | n, p t. Multiplicative and bilinear complexity of A equal to 2n − t.
منابع مشابه
On dimension of a special subalgebra of derivations of nilpotent Lie algebras
Let $L$ be a Lie algebra, $mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$. We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields. Also, we classi...
متن کاملOn the Parameterization of Primitive Ideals in Affine Pi Algebras
In their fundamental studies of the finite dimensional representations of associative algebras, Artin and Procesi proved that the primitive ideals corresponding to irreducible n-dimensional representations (for fixed n, over an algebraically closed field) can be homeomorphically parameterized by a locally closed subset of the maximal spectrum of a suitably chosen affine commutative trace ring. ...
متن کاملFine Gradings on Simple Classical Lie Algebras
The fine abelian group gradings on the simple classical Lie algebras (including D4) over algebraically closed fields of characteristic 0 are determined up to equivalence. This is achieved by assigning certain invariant to such gradings that involve central graded division algebras and suitable sesquilinear forms on free modules over them.
متن کاملHow to Expand the Zariski Topology
We introduce the notion of a Hu-Liu prime ideal in the context of left commutative rngs, and establish the contravariant functor from the category of left commutative rngs into the category of topological spaces. It is well known that new points must be introduced in order to expand algebraic geometry over algebraically closed fields into Grothendieck’s scheme theory over commutative rings. We ...
متن کاملIsomorphism Types of Commutative Algebras of Finite Rank over an Algebraically Closed Field
Let k be an algebraically closed field. We list the finitely many isomorphism types of rank n commutative k-algebras for n ≤ 6. There are infinitely many types for each n ≥ 7. All algebras are assumed to be commutative, associative, and with 1 (except briefly in Remark 1.1). We assume that k is an algebraically closed field, except in Section 2. By the rank of a k-algebra, we mean its dimension...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007