منابع مشابه
Multiplicative Invariants and Semigroup Algebras
Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S = k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.
متن کاملClass Groups of Multiplicative Invariants
Let G be a nite subgroup of GL d (Z). Then G acts on the Laurent polynomial ring kX 1 1 d ] over the eld k via the natural G-action on the multiplicative group generated by the variables X 1 ; : : : ; X d (= Z d). We show that the class group of the ring of invariants of this action is isomorphic to Hom(G=N;k) H 1 (G=D; (Z d) D), where N denotes the subgroup of G that is generated by all reeect...
متن کاملSagbi Bases in Rings of Multiplicative Invariants
Let k be a field and G be a finite subgroup of GLn(Z). We show that the ring of multiplicative invariants k[x±1 1 , . . . , x ±1 n ] G has a finite SAGBI basis if and only if G is generated by reflections.
متن کاملcomparing the second multiplicative zagreb coindex with some graph invariants
the second multiplicative zagreb coindex of a simple graph $g$ is defined as: $${overline{pi{}}}_2left(gright)=prod_{uvnotin{}e(g)}d_gleft(uright)d_gleft(vright),$$ where $d_gleft(uright)$ denotes the degree of the vertex $u$ of $g$. in this paper, we compare $overline{{pi}}_2$-index with some well-known graph invariants such as the wiener index, schultz index, eccentric co...
متن کاملOn the Cohen-macaulay Property of Multiplicative Invariants
We investigate the Cohen-Macaulay property for rings of invariants under multiplicative actions of a finite group G. By definition, these are G-actions on Laurent polynomial algebras k[x 1 , . . . , x ±1 n ] that stabilize the multiplicative group consisting of all monomials in the variables xi. For the most part, we concentrate on the case where the base ring k is Z. Our main result states tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90028-7