Related papers: Invariant states on noncommutative tori

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

Given an abelian group G endowed with a T-pre-symplectic form, we assign to it a symplectic twisted group *-algebra W_G and then we provide criteria for the uniqueness of states invariant under the ergodic action of the symplectic group of…

Let $s$ be a fixed hyperelliptic involution of the closed, oriented genus $g$ surface $\Sigma_g$. The hyperelliptic Torelli group $\mathcal{SI}_g$ is the subgroup of the mapping class group $\mathrm{Mod}(\Sigma_g)$ consisting of elements…

To every $Q$-irreducible representation $r$ of a finite group $H$, there corresponds a simple factor $A$ of $Q[H]$ with an involution $\tau$. To this pair $(A,\tau)$, we associate an arithmetic group $\Omega$ consisting of all $(2g-2)\times…

Let $G$ be a simply connected compact Lie group and $\mathscr{L}$ be the left invarinat framing of $G$. Let $\mathcal{L}^\lambda$ be the framing obtained by twisting $\mathscr{L}$ by a faithful representation $\lambda$. Given a torus…

Let $\alpha\colon G\curvearrowright A$ be an action of a countable discrete group on a separable unital $C^*$-algebra. We study the simplex $\mathrm{T}(A)^G$ of $G$-invariant traces and ask when it is Bauer. Our main result is a…

We develop the theory of quasi--invariant (resp. strongly quasi--invariant) states under the action of a group $G$ of normal $*$--automorphisms of a $*$--algebra (or von Neumann alegbra) $\mathcal{A}$. We prove that these states are…

We consider a set $SPG(\mathcal{A})$ of pure split states on a quantum spin chain $\mathcal{A}$ which are invariant under the on-site action $\tau$ of a finite group $G$. For each element $\omega$ in $SPG(\mathcal{A})$ we can associate a…

This article is a continuation of [Kub18], which proves that if a $3$-dimensional affine normal quasihomogeneous $SL(2)$-variety $E$ is toric, then it has an equivariant resolution of singularities given by an invariant Hilbert scheme…

We provide sufficient conditions for the existence of a trace on the essential $\mathrm{C}^\ast$-algebra of a (not necessarily Hausdorff) \'etale groupoid $G$ which extends an invariant measure $\mu$ on the unit space of $G$. In particular,…

We generalize the theory of the second invariant cohomology group $H^2_{\rm inv}(G)$ for finite groups $G$, developed in [Da2,Da3,GK], to the case of affine algebraic groups $G$, using the methods of [EG1,EG2,G]. In particular, we show that…

In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only…

The Torelli group of $W_g = \#^g S^n \times S^n$ is the subgroup of the diffeomorphisms of $W_g$ fixing a disc which act trivially on $H_n(W_g;Z)$. The rational cohomology groups of the Torelli group are representations of an arithmetic…

Let $S_g$ ($g\geq 2$) be a closed surface of genus $g$. Let $K$ be any real number field and $A$ be any quaternion algebra over $K$ such that $A\otimes_K\mathbb{R}\cong M_2(\mathbb{R})$. We show that there exists a hyperbolic structure on…

Let I_g,* denote the (pointed) Torelli group. This is the group of homotopy classes of homeomorphisms of the genus g >= 2 surface S_g with a marked point, acting trivially on H := H_1(S_g). In 1983 Johnson constructed a beautiful family of…

Given a topological graph $E$, we give a complete description of tracial states on the C*-algebra $\mathrm{C}^*(E)$ which are invariant under the gauge action; there is an affine homeomorphism between the space of gauge invariant tracial…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geq 0$ and let $V$ be an irreducible rational $G$-module with highest weight $\lambda$. When $V$ is self-dual, a basic question to ask…

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state.

This is a continuation of our paper math.AG/0111298. We prove an explicit formula for the geometric genus p_g of a quasihomogeneous isolated surface singularity in terms of the Seiberg-Witten invariant of the link and other topological data…

Let $k$ be a field, let $G$ be a reductive group, and let $V$ be a linear representation of $G$. Let $V//G = Spec(Sym(V^*))^G$ denote the geometric quotient and let $\pi: V \to V//G$ denote the quotient map. Arithmetic invariant theory…