symmetric monoidal (∞,1)-category of spectra
An -algebra is an ∞-algebra over the E-k operad.
-algebras are often called A-∞ algebras. See also algebra in an (∞,1)-category.
An algebra in the symmetric monoidal (∞,1)-category Spec of spectra is a ring spectrum.
The homology of an -algebra in chain complexes is a Gerstenhaber algebra.
See E-∞ algebra.
The homology of an -algebra for is a Poisson n-algebra.
Moreover, in chain complexes over a field of characteristic 0 the E-n operad is formal, hence equivalent to its homology, and so in this context -algebras are equivalent to Poisson n-algebras.
See there for more.
Section 5 of
some summary of which is at Ek-Algebras.
Discussion of derived noncommutative geometry over formal duals of -algebras is in
John Francis, Derived algebraic geometry over -Rings (pdf)
John Francis, The tangent complex and Hochschild cohomology of -rings (pdf)
Last revised on June 25, 2022 at 19:04:33. See the history of this page for a list of all contributions to it.