K-Theory of Stable Generalized Operator Algebras

It is proved that algebraic and topological K-functors are isomorphic on the category of stable generalized operator algebras which are K _i -regular for all i > 0.     

N -Fold ?ech Derived Functors and Generalised Hopf Type Formulas

The notion of n-fold Čech derived functors is introduced and studied. This is illustrated using the n-fold Čech derived functors of the nilization functors Z_k. This gives a new purely algebraic method for the investigation of the Brown–Ellis generalised Hopf formula for the higher integral group homology and for its further generalisation. The paper ends with an application to algebraic K-theory. (Received: December 2004)     

Non-Abelian Cohomology of Groups

Following Guin's approach to non-abelian cohomology [4] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology up to dimension 2     

Homology of -types and Hopf type formulas

The tripleability of the category of crossed n-cubes is studied. The leading cotriple homology of these homotopy (n+1)-types is investigated, describing it as Hopf type formulas.     

Exact sequences in homology of multiplicative Lie rings and a new version of Stallings' theorem

We show that the non-abelian tensor product of nilpotent, solvable and Engel multiplicative Lie rings is nilpotent, solvable and Engel, respectively. The six term exact sequence in homology of multiplicative Lie rings is obtained. We also prove a new version of Stallings' theorem.     

Categorical interpretations of some key agreement protocols

We give interpretations of some known key agreement protocols in the framework of category theory and in this way we propose a method of constructing of many new key agreement protocols.     

Homological aspects of Lie algebra crossed modules

Internal homology theory in the category of crossed modules of Lie algebras is constructed and investigated. Its relationship with the Chevalley-Eilenberg homology is established in terms of a long exact homology sequence.     

Non-Abelian Cohomology with Coefficients in Crossed Bimodules

When the coefficients are crossed bimodules, Guin's non-abelian cohomology [2], [3] is extended in dimensions 1 and 2, and a nine-term exact cohomology sequence is obtained.     

Algebraic K-theory of Normed Algebras

Quillen's algebraic K-theory of discrete rings is extended to the category of normed algebras over a commutative Banach ring k with unit and its relationship with topological K-theory is established. Sufficient conditions for the isomorphism of algebraic and topological K-groups on the category of real normed algebras are given. The isomorphism of algebraic and topological K-functors on the category of polynomial extensions of stable C-algebras is proved.