D-algebras and D G-interior algebras

Abstract

Following Bernhard Keller [13], a differential Z -graded O-algebra or, in short, a D-algebra is an O-algebra A endowed with a differential Z-graded O-module structure (see Remark 10.5 above) such that the product map A ⊗o A → A is D-linear or, equivalently, such that, for any a, a’ ∈ A and any ∈ℱ,we have (cf. 10.2.3)

EquationSource$$\[f\left( {aa’} \right) = \sum\limits_{z,z’ \in Z} {f\left( z \right)} {i_{z’}}\left( a \right){i_z} - \left( {a’} \right)\]$$

(11.1.1)

EquationSource$$\[d\left( {aa’} \right) = d\left( a \right)s\left( {a’} \right) + ad\left( {a’} \right)\]$$

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