nLab curved A-infinity algebra

Idea

A curved $A_\infty$ is defined just like an A-infinity algebra, but allowing in the definition also a 0-ary operation. $m_0$. Including this means the unary operation no longer squares to 0 but to be proportional to the binary product with this constant

$$m_1 \circ m_1 \propto m_2(m_0,-) \,.$$

This $m_0$ is called the curvature of the curved $A_\infty$-algebra.

Examples

• The curved BGG sequences under cup product yield curved $A_\infty$-algebras (Calderbank-Diemer 00, section 6).

Related concepts

• curved dg-algebra

• curved L-infinity algebra

References

• David Calderbank, Tammo Diemer, Differential invariants and curved Bernstein-Gelfand-Gelfand sequences, J.Reine Angew.Math. 537 (2001) 67-103 (arXiv:math/0001158)