Search arXivSearch

arXiv · 1808.04903

Noncommutative Bialynicki-Birula Theorem

Abstract

In this short note we prove that every maximal torus action on the free algebra is conjugate to a linear action. This statement is the free algebra analogue of a classical theorem of A. Białynicki-Birula.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Andrey Elishev, Alexei Kanel-Belov, Farrokh Razavinia, Jie-Tai Yu, Wenchao Zhang. 2019-06-05. Noncommutative Bialynicki-Birula Theorem. https://doi.org/10.22405/2226-8383-2020-21-1-51-61

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG