相关论文: Identifying JBW$^*$-algebras through their spheres…

$W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebras are deformations of ${\mathfrak{bms}_3}$ and ${\mathfrak{bms}_4}$ algebra respectively. We present an $\mathcal{N}=2$ supersymmetric extension of $W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebra…

We consider the problem of classifying irreducible Specht modules for the Iwahori-Hecke algebra of type B with parameters Q,q. We solve this problem completely in the case where q is not a root of unity, and in the case q=-1 we reduce the…

We prove the longstanding physics conjecture that there exists a unique two-parameter $\mathcal{W}_{\infty}$-algebra which is freely generated of type $\mathcal{W}(2,3,\dots)$, and generated by the weights $2$ and $3$ fields. Subject to…

We find a substantial class of pairs of $*$-homomorphisms between graph C*-algebras of the form $C^*(E)\hookrightarrow C^*(G)\twoheadleftarrow C^*(F)$ whose pullback C*-algebra is an AF graph C*-algebra. Our result can be interpreted as a…

We generalize the main theorem of Rieffel for Morita equivalence of W*-algebras to the case of unital dual operator algebras: two unital dual operator algebras A and B have completely isometric normal representations alpha, beta such that…

Motivated by deformation quantization we consider $^*$-algebras over ordered rings and their deformations: we investigate formal associative deformations compatible with the $^*$-involution and discuss a cohomological description in terms…

We prove nonuniqueness results for complete metrics with constant positive fractional curvature conformal to the round metric on $S^n \setminus S^k$, using bifurcation techniques. These are singular (positive) solutions to a non-local…

Let $p(z,w)$ be a polynomial in two variables. We call the solution of the algebraic equation $p(z,w) = 0$ the algebraic correspondence. We regard it as the graph of the multivalued function $z \mapsto w$ defined implicitly by $p(z,w) = 0$.…

Let $V$ be the two-dimensional simple module and $M$ be a projective Verma module for the quantum group of $\mathfrak{sl}_2$ at generic $q$. We show that for any $r\ge 1$, the endomorphism algebra of $M\otimes V^{\otimes r}$ is isomorphic…

We show that given a rigid C*-tensor category, there is an equivalence of categories between normalized irreducible Q-systems, also known as connected unitary Frobenius algebra objects, and compact connected W*-algebra objects. Although…

The seminal theorem of I.J. Schoenberg characterizes positive definite (p.d.) kernels on the unit sphere $S^{n-1}$ invariant under the automorphisms of the sphere. We obtain two generalizations of this theorem for p.d. kernels on fiber…

Let $k$ be an algebraically closed field, $\mathop{char}(k) = p \geq 2$ and $E_r$ be a $p$-elementary abelian group of rank $r \geq 2$. Let $(c,d) \in \mathbb{N}^2$. We show that there exists an indecomposable module of constant Jordan type…

Let $B$ be a Borel subgroup of a semisimple algebraic group $G$, and let $\mathfrak a$ be an abelian ideal of $\mathfrak b=Lie(B)$. The ideal $\mathfrak a$ is determined by certain subset $\Delta_{\mathfrak a}$ of positive roots, and using…

The positive part $U^+_q$ of $U_q(\widehat{\mathfrak{sl}}_2)$ has a presentation with two generators $A,B$ that satisfy the cubic $q$-Serre relations. We introduce a PBW basis for $U^+_q$, said to be alternating. Each element of this PBW…

As a sequel to [14], in this article we first introduce a so-called duplex Hecke algebras of type B which is a Q(q)-algebra associated with the Weyl group W (B) of type B, and symmetric groups S_l for l = 0, 1, . . . ,m, satisfying some…

In previous work, we proposed a general framework of positive topological field theories (TFTs) based on Eilenberg's notion of summation completeness for semirings. In the present paper, we apply this framework in constructing explicitly a…

We prove that every surjective isometry from the unit sphere of a rank-2 Cartan factor $C$ onto the unit sphere of a real Banach space $Y$, admits an extension to a surjective real linear isometry from $C$ onto $Y$. The conclusion also…

We investigate reflection-type problems on the class SPM, of Boolean algebras carrying strictly positive finitely additive measures. We show, in particular, that in the constructible universe there is a Boolean algebra $\mathfrak A$ which…

We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements of infinite order in higher homotopy and homology groups of these spaces, which,…

Let $p$ be a prime and let $G$ be a finite group. By a celebrated theorem of Swan, two finitely generated projective $\mathbb Z_p[G]$-modules $P$ and $P'$ are isomorphic if and only if $\mathbb Q_p \otimes_{\mathbb Z_p} P$ and $\mathbb Q_p…