For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given. Under some technical assumptions it is proved that Woronowicz’ external algebra of left-invariant differential forms either contains a unique form of maximal degree or it is infinit...

This paper is a study of derivations on unbounded operator algebras in connection with those in operator algebras. In particular we study spatiality of derivations in several situations. We give the characterization of derivations on general «-algebras by using positive linear functionals. We also show that a derivation with some range-property on a left ■EW*-algebra induced by an unbounded Hub...

In this paper, we mainly discuss linear deformations of a Hom-Lie-Yamaguti algebra and introduce the notion Hom-Nijenhuis operator. We product structure on algebra, which is operator E satisfying E2 = Id. There an involutive if only direct sum two subalgebras (as vector spaces). At same time, also complex algebra. Finally, add compatibility condition between to