Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HC(A) of A and the Banach B-relative cyclic cohomology group HCnB(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HC(A) = HCnB(A) ...

HODGE DECOMPOSITION AND MINIMAL MODELS FOR CYCLIC ALGEBRAS J. CHUANG AND A. LAZAREV Abstract. We show that an algebra over a cyclic operad supplied with an additional linear We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal m...

Let p be a prime integer and F the function field in two algebraically independent variables over smaller F0. We prove that if char(F0)=p⩾3 then there exist p2−1 cyclic algebras of degree have no maximal subfield common, char(F0)=0 p2 common.