On homology of Lie algebras over commutative rings

Separable Algebras over Commutative Rings

Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...

Dual coalgebras of algebras over commutative rings

In the study of algebraic groups the representative functions related to monoid algebras over fields provide an important tool which also yields the finite dual coalgebra of any algebra over a field. The purpose of this note is to transfer this basic construction to monoid algebras over commutative rings R. As an application we obtain a bialgebra (Hopf algebra) structure on the finite dual of t...

On the Cyclic Homology of Commutative Algebras over Arbitrary Ground Rings

On the Cyclic Homology of Commutative Algebras over Arbitrary Ground Rings

The algebra ΛV ⊗ Γ(dV ) is a divided power version of the de Rham algebra; in the particular case when k is a field of characteristic zero, the spectral sequences above agree with those found in [BuV], where it is shown they degenerate at the E term. For arbitrary ground rings we prove here (theorem 2.3) that if Vn = 0 for n ≥ 2 then E = E. From this we derive a formula for the Hochschild homol...

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.