Homotopy epimorphisms and derived tate’s acyclicity for commutative<i>C</i>*-algebras

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

Homotopy Leibniz Algebras and Derived Brackets

We will discuss a bar/coalgebra construction of strong homotopy Leibniz algebras. We will give a generalized framework of derived bracket construction. We will prove that a deformation derivation of differential graded Leibniz algebra induces a strong homotopy Leibniz algebra by derived bracket method.

Epimorphisms onto Derivation Algebras

We prove that the separating space of an epimorphism from a Lie–Banach algebra onto the (continuous) derivation algebra Der(A) of a Banach algebra A consists of derivations which map into the radical of A.

On Epimorphisms and Monomorphisms of Hopf Algebras

We notice that for a Hopf algebra H , its antipode S is both an epimorphism and a monomorphism from H to H in the category of Hopf algebras over a field. Together with the existence of Hopf algebras with non-injective or non-surjective antipode, this proves the existence of non-surjective epimorphisms and non-injective monomorphisms in the category of Hopf algebras. Using Schauenburg’s free Hop...

Homotopy Dg Algebras Induce Homotopy Bv Algebras

Let TA denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then TA is a differential BatalinVilkovisky algebra. Moreover, if A is an A∞ algebra, then TA is a commutative BV∞ algebra. 1. Main Statement Let (A, dA) be a complex over a commutative ring R. Our convention is that dA is of degree +1. The space TA ...