On $$C^*$$-norms on $${{\mathbb {Z}}}_2$$-graded tensor products

We systematically investigate $$C^*$$ C ∗ -norms on the algebraic graded product of $${{\mathbb {Z}}}_2$$ Z 2 -graded $$C^*$$ C ∗ -algebras. This requires to single out the notion of a compatible norm, that is a norm with respect to which the product grading is bounded. We then focus on the spatial norm proving that it is minimal among all compatible $$C^*$$ C ∗ -norms. To this end, we first show that commutative $${{\mathbb {Z}}}_2$$ Z 2 -graded $$C^*$$ C ∗ -algebras enjoy a nuclearity property in the category of graded $$C^*$$ C ∗ -algebras. In addition, we provide a characterization of the extreme even states of a given graded $$C^*$$ C ∗ -algebra in terms of their restriction to its even part.

Torsion for Homological Complexes of Nonassociative Algebras with Metagroup Relations

The article is devoted to homological complexes and modules over nonassociative algebras with metagroup relations. Smashed tensor products of them are studied. Their torsions and homomorphisms are investigated.

Group graded Morita equivalences for wreath products

"Starting with group graded Morita equivalences, we obtain Morita equivalences for tensor products and wreath products."