The stub for “associative” bialgebroid. Bialgebroids are to bialgebras what on dual side groupoids are to groups. More references at Hopf algebroids.

]]>New entry noncommutative differential calculus with redirect Batalin-Vilkovisky module.

]]>We have just posted to the arXiv ours

- S. Meljanac, Z. Škoda,
*Lie algebra type noncommutative phase spaces are Hopf algebroids*, arxiv/1409.8188

This paper is in an algebraic approach; the related geometric picture as well as a paper on a relation to Lie algebra automorphisms are in preparation.

]]>stub tertiary radical with redirects third radical, tertiary decomposition theory

]]>noncommutative rational functions under construction

]]>There is a new stub E-theory with redirect asymptotic morphism, new entry semiprojective morphism (of separable $C^\ast$-algebras) and stub Brown–Douglas–Fillmore theory, together with some recent bibliography&links changes at Marius Dadarlat, shape theory etc. There should be soon a separate entry shape theory for operator algebras but I still did not do it.

]]>Urs, David Roberts and I got into discussion of locally trivial noncommutative bundles in a discussion with a wrong title (see around here), so let us better move it here. There are still some of my latest posts there which Urs and David might have not yet seen.

I decided to update a bit noncommutative principal bundle, so I will start today a bit.

]]>Stub for connection in noncommutative geometry.

]]>New entry spectral cookbook with sketch of some *very* nice constructions of A. Rosenberg. New stub sheaf on a noncommutative space, pretty contentless so far, and a redirect page noncommutative sheaf, where the latter may have a different meaning (that is why a separate page).

New stubs noncommutative projective geometry and Michael Artin.

]]>New entry defining ideal of topologizing subcategory (of an abelian category), wanted at conormal bundle. It is in fact a subfunctor of the identity functor and if we evaluate it on projective generator in the case of a module category then we get the usual ideal in the corresponding ring.

]]>I started an important entry differential monad. According to Lunts-Rosenberg MPI 1996-53 pdf differential calculus on schemes and noncommutative schemes can be derived from the yoga of coreflective topologizing subcategories in the abelian category of quasicoherent sheaves on the scheme, like the $\mathbb{T}$-filtration, and $\mathbb{T}$-part, in the case when the topologizing subcategory is the diagonal in the sense of the smallest subcategory of the category of additive endofunctors having right adjoint which contains the identity functor – in that case we say differential filtration and differential part. The regular differential operators are the elements of the differential part of the bimodule of endomorphisms. Similarly, one can define the conormal bundle etc.

]]>I have created degeneration conjecture required at Dmitri Kaledin. In my memory, I never heard ofthis **degeneration conjecture** by precisely *that* name and I do not like it (there are so many degeneration conjectures in other fields, some of which I heard under *that* name). It is usually said the **degeneration of Hodge to de Rham spectral sequence** (conjecture). It has a classical analogue. I put redirect degeneration of Hodge to de Rham spectral sequence.

New stub model structure on operator algebras with redirects model structures on operator algebras, homotopy theory for operator algebras, homotopy theory for C*-algebras etc.

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