Related papers: Berezin expectation and Clifford trace

For an irreducible conic $\mathcal C$ in a Desarguesian plane of odd square order, estimating the number of points from a Baer subplane which are external to $\mathcal C$ is a natural problem. In this paper, a complete list of possibilities…

We study the structure of the codifferent and of additively indecomposable integers in families of totally real cubic fields. We prove that for cubic orders in these fields, the minimal trace of indecomposable integers multiplied by totally…

We give a conceptual explanation for the somewhat mysterious origin of Suslin matrices. This enables us to generalize the construction of Suslin matrices and to give more conceptual proofs of some well-known results.

We study the problem of extending a state on an abelian $C^*$- subalgebra to a tracial state on the ambient $C^*$-algebra. We propose an approach that is well-suited to the case of regular inclusions, in which there is a large supply of…

This letter establishes a procedure which can determine an algebra of exotic particles obeying fractional statistics and living in two-dimensional space using a non-commuting coordinates.

Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the direction of investigation had, as far as we can discern, all followed the ordinary Euclidean…

We consider the diffeological pseudo-bundles of exterior algebras, and the Clifford action of the corresponding Clifford algebras, associated to a given finite-dimensional and locally trivial diffeological vector pseudo-bundle, as well as…

The forcing relation of braids has been introduced for a 2-dimensional analogue of the Sharkovskii order on periods for maps of the interval. In this paper, by making use of the Nielsen fixed point theory and a representation of braid…

The main result of the paper is a description of conormal Lie algebras of Feigin-Odesskii Poisson structures. In order to obtain it we introduce a new variant of a definition of a Feigin-Odesskii Poisson structure: we define it using a…

Starting with a symmetric/antisymmetric matrix with integer coefficients (which we view as an analogue of a metric/form on a principal bundle over the "manifold" Spec Z) we introduce arithmetic analogues of Chern connections and their…

We introduce and study the notion of an outer bi-Lipschitz extension of a map between Euclidean spaces. The notion is a natural analogue of the notion of a Lipschitz extension of a Lipschitz map. We show that for every map $f$ there exists…

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and Vinogradov, and we prove that…

Using the techniques developed in arxiv: 1203.3544 we compute the universal part of the equilibrium partition function characteristic of a theory with multiple abelian U(1) anomalies in arbitrary even spacetime dimensions. This contribution…

This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and…

We introduce a bt-algebra of type B. We define this algebra doing the natural analogy with the original construction of the bt-algebra. Notably we find a basis for it, a faithful tensorial representation, and we prove that it supports a…

We construct a framework within which a mathematically precise, fully covariant, and exact averaging procedure for tensor fields on a manifold can be formulated. In particular, we introduce the Weitzenb\"ock connection for parallel…

We give details of a formerly known relation between ternary quadratic forms and quaternion orders through the even Clifford algebra. Based on this and classifications of ternary quadratic forms we give a completely explicit classification…

To a regular projection of a knot we associate a finite dimensional non-commutative associative algebra which is self-injective and special biserial.

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum…

A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…