相关论文: Rational Formulas for Traces in zero-dimensional A…

Let $\alpha$ be a totally positive algebraic integer, and define its absolute trace to be $\frac{Tr(\alpha)}{\text{deg}(\alpha)}$, the trace of $\alpha$ divided by the degree of $\alpha$. Elementary considerations show that the absolute…

The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. We give a uniform trigonometric $R$-matrix for…

A matrix model for type 0 strings is proposed. It consists in making a non-supersymmetric orbifold projection in the Yang-Mills theory and identifying the infrared configurations of the system at infinite coupling with strings. The correct…

In the spirit of Arthur's trace formula, we establish a general trace formula for symmetric spaces associated with the variety of involutions of a finite $D$-module where $D$ is a division algebra central over a number field $F$. Such a…

In this paper we describe the defining equations of the Rees algebra and the special fiber ring of a truncation I of a complete intersection ideal in a polynomial ring over a field with homogeneous maximal ideal m. To describe explicitly…

We study the Poincar\'e series of the mixed and pure trace rings of generic matrices. These series are known to be rational functions. We obtain an explicit formula in lowest terms in the case of $2\times2$ matrices; a denominator, which we…

In this paper, we present a complete classification of 2-dimensional endo-commutative straight algebras of type II$_1$ over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves…

Given any separable complex Hilbert space, any trace-class operator $B$ which does not have purely imaginary trace, and any generator $L$ of a norm-continuous one-parameter semigroup of completely positive maps we prove that there exists a…

Mean dimension for AH-algebras is introduced. It is shown that if a simple unital AH-algebra with diagonal maps has mean dimension zero, then it has strict comparison on positive elements. In particular, the strict order on projections is…

Let $\mathcal{A}$ be a unital algebra, $\delta$ be a linear mapping from $\mathcal{A}$ into itself and $m$, $n$ be fixed integers. We call $\delta$ an (\textit{m, n})-derivable mapping at $Z$, if…

We present an explicit formula for computing toric residues as a quotient of two determinants, a la Macaulay, where the numerator is a minor of the denominator. We also give an irreducible representation of toric residues by extending the…

Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…

Let (A,phi) be the reduced free product of infinitely many pairs (A_i,phi_i) of C*-algebras with faithful states. Assume that the A_i are not too small, in a specific sense. It is shown that if phi is a trace then K_0(A) is determined…

In order to circumvent a fundamental issue when studying densely defined traces on $\mathrm{C}^\ast$-algebras -- which we refer to as the Trace Question -- we initiate a systematic study of the set $T_{\mathbb R}(A)$ of self-adjoint traces…

In an unpublished note [H1] we have described a method to obtain a formula for the index of an analytic vector field with (complex) isolated zero on a real analytic hypersurface with (complex) isolated singularity. This formula, like the…

Let $(R,{\frak{m}}_R)$ be a commutative noetherian local ring. Assuming that ${\frak{m}}_R=$$I\oplus J$ is a direct sum decomposition, where $I$ and $J$ are non-zero ideals of $R$, we describe the structure of the Tor algebra of $R$ in…

We describe a self-contained procedure for constructing the traceless projection of mixed tensor products (built out of a finite-dimensional complex vector space and its dual). The construction relies on the Schur-Weyl duality for the…

In this note, we show that the decomposition group $Dec(I)$ of a zero-dimensional radical ideal $I$ in ${\bf K}[x_1,\ldots,x_n]$ can be represented as the direct sum of several symmetric groups of polynomials based upon using Gr\"{o}bner…

According to an old result of Albert and Muckenhoupt, the commutators in the endomorphism ring of a finite dimensional vector space are precisely the elements of trace zero. We replace the finite dimensional vector space with a complex of…

By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In…