Related papers: Relative-partitioned index theorem

It is proven that in the universal splitexact equivariant algebraic $KK$-theory for algebras, the $K$-theory groups coincide with classical $K$-theory in the sense of Phillips. This partially answers a question raised by Kasparov.

We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.

We introduce a new class of symmetric space orbital integrals important for applications in certain relative trace formulas appearing in the theory of automorphic representations. We verify a fundamental lemma for $U_2\times…

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.

In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).

We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor,…

We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian…

In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…

In this paper, we first prove a theorem by a little modification on the Lax-Milgram theorem. Then, using $K$-frames, we obtain lower and upper bounds for the results obtained from this theorem. Also, we present some methods for the…

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…

This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence…

Let G denote a split simply connected almost simple p-adic group. The classical example is the special linear group SL(n). We study the K-theory of the unramified unitary principal series of G and prove that the rank of K_0 is the…

We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version…

We develop a finite KKG-theory of C*-algebras following Arlettaz- H.Inassaridze's approach to finite algebraic K-theory. The Browder- Karoubi-Lambre's theorem on the orders of the elements for finite algebraic K-theory is extended to finite…

The prototype of mutually independent systems are systems which are localized in spacelike separated regions. In the framework of locally covariant quantum field theory we show that the commutativity of observables in spacelike separated…

We define a group of relative differential K-characters associated with a smooth map between two smooth compact manifolds. We show that this group fits into a short exact sequence as in the non-relative case. Some secondary geometric…

In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.

We give a general formula for the equivariant complex $K$-theory $K_G^*(V)$ of a finite dimensional real linear space $V$ equipped with a linear action of a compact group $G$ in terms of the representation theory of a certain double cover…