相关论文: Dilation Theory for Rank 2 Graph Algebras

Given a row-finite $k$-graph $\Lambda$ with no sources we investigate the $K$-theory of the higher rank graph $C^*$-algebra, $C^*(\Lambda)$. When $k=2$ we are able to give explicit formulae to calculate the $K$-groups of $C^*(\Lambda)$. The…

J. Renault has recently found a generalization of the caracterization of C*-diagonals obtained by A. Kumjian in the eighties, which in turn is a C*-algebraic version of J. Feldman and C. Moore's well known Theorem on Cartan subalgebras of…

The article deals with isometric dilation and commutant lifting for a class of $n$-tuples $(n \geq 3)$ of commuting contractions. We show that operator tuples in the class dilate to tuples of commuting isometries of BCL type. As a…

The isometric dilation of a pair of commuting contractions due to And\^{o} is not minimal. We modify And\^{o}'s dilation and construct a minimal isometric dilation on $\mathcal H \oplus_2 \ell_2(\mathcal H \oplus_2 \mathcal H)$ for a…

This note records some dilation theorems about contraction semigroups on a Hilbert space - all of which fall into the categories "known" or "probably known" - that I proved while working on my PhD in mathematics (under the supervision of…

We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the…

We characterize Beurling quotient subspaces for pure doubly commuting isometric representations of product systems. As a consequence, we derive a concrete regular dilation theorem for a pure completely contractive covariant representation…

We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a…

Understanding the metric structure of permutation families is fundamental to combinatorics and has applications in social choice theory, bioinformatics, and coding theory. We study permutation families defined by restriction…

We develop the representation theory of shifted quantum affine algebras $\mathcal{U}_q^\mu(\hat{\mathfrak{g}})$ and of their truncations which appeared in the study of quantized K-theoretic Coulomb branches of 3d $N = 4$ SUSY quiver gauge…

We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is…

The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters. Through the recent "categorifications" of cluster algebras using representation theory one obtains a whole variety of exchange graphs associated…

The Weyl algebra (W_{2m}[h]; *) is the algebra generated by u=(u_1,...,u_m,v_1,.....,v_m) over C with the fundamental commutation relation [u_i,v_j]=-ih\delta_{ij}, where h is a positive constant. The Heisenberg algebra (\Cal H_{2m}[nu];*)…

We develop invariant theory for the quantum group ${\rm U}_q$ of $G_2$ at generic $q$ in the setting of braided symmetric algebras. Let ${\mathcal A}_m$ be the braided symmetric algebra over $m$-copies of the $7$-dimensional simple ${\rm…

We study the deformation theory of morphisms of properads and props thereby extending to a non-linear framework Quillen's deformation theory for commutative rings. The associated chain complex is endowed with a Lie algebra up to homotopy…

We study two well-known $SU(N)$ chiral gauge theories with fermions in the symmetric, anti-symmetric and fundamental representations. We give a detailed description of the global symmetry, including various discrete quotients. Recent work…

In this paper, we study multiplicative structures on the K-theory of the core $A:=C^*(E)^{U(1)}$ of the C*-algebra $C^*(E)$ of a directed graph $E$. In the first part of the paper, we study embeddings $E\to E\times E$ that induce a…

We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental…

We define a new topological polynomial extending the Bollobas-Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behavior under partial duality. This allows to write down a completely…

For a tuple $T$ of Hilbert space operators, the 'commuting dilation constant' is the smallest number $c$ such that the operators of $T$ are a simultaneous compression of commuting normal operators of norm at most $c$. We present numerical…