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The $G$ -graded identities of the Grassmann Algebra

Lucio Centrone (2016)

Archivum Mathematicum

Let $G$ be a finite abelian group with identity element $1_{G}$ and $L = ⨁_{g \in G} L^{g}$ be an infinite dimensional $G$ -homogeneous vector space over a field of characteristic $0$ . Let $E = E (L)$ be the Grassmann algebra generated by $L$ . It follows that $E$ is a $G$ -graded algebra. Let $| G |$ be odd, then we prove that in order to describe any ideal of $G$ -graded identities of $E$ it is sufficient to deal with $G^{'}$ -grading, where $| G^{'} | \leq | G |$ , ${dim}_{F} L^{1_{G^{'}}} = \infty$ and ${dim}_{F} L^{g^{'}} < \infty$ if $g^{'} \neq 1_{G^{'}}$ . In the same spirit of the case $| G |$ odd, if $| G |$ is even it is sufficient to study only those $G$ -gradings such that...

The Galois algebras and the Azumaya Galois extensions.

Szeto, George, Xue, Lianyong (2002)

International Journal of Mathematics and Mathematical Sciences

The Galois extensions induced by idempotents in a Galois algebra.

Szeto, George, Xue, Lianyong (2002)

International Journal of Mathematics and Mathematical Sciences

The general Ikehata theorem for $H$ -separable crossed products.

Szeto, George, Xue, Lianyong (2000)

International Journal of Mathematics and Mathematical Sciences

The geometric reductivity of the quantum group $S L_{q} (2)$

Michał Kępa, Andrzej Tyc (2011)

Colloquium Mathematicae

We introduce the concept of geometrically reductive quantum group which is a generalization of the Mumford definition of geometrically reductive algebraic group. We prove that if G is a geometrically reductive quantum group and acts rationally on a commutative and finitely generated algebra A, then the algebra of invariants $A^{G}$ is finitely generated. We also prove that in characteristic 0 a quantum group G is geometrically reductive if and only if every rational G-module is semisimple, and that in...