Related papers: $q$-invariance of quantum quaternion spheres

We study the quantum sphere $C_q[S^2]$ as a quantum Riemannian manifold in the quantum frame bundle approach. We exhibit its 2-dimensional cotangent bundle as a direct sum $\Omega^{0,1}\oplus\Omega^{1,0}$ in a double complex. We find the…

Continuing our project on noncommutative (stable) homotopy we construct symmetric monoidal $\infty$-categorical models for separable $C^*$-algebras $\mathtt{SC^*_\infty}$ and noncommutative spectra $\mathtt{NSp}$ using the framework of…

Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms…

Let A be a commutative unital algebra over an algebraically closed field k of characteristic not equal to 2, whose generators form a finite-dimensional subspace V, with no nontrivial homogeneous quadratic relations. Let Q be a Hopf algebra…

The non commuting matrix elements of matrices from quantum group $GL_q(2;C)$ with $q\equiv \omega $ being the $n$-th root of unity are given a representation as operators in Hilbert space with help of $C_4^{(n)}$ generalized Clifford…

We prove that every non-constant quasiregular selfmap of the $n$-sphere $\mathbb{S}^{n}$ admits a harmonic extension to the hyperbolic space $\mathbb{H}^{n+1}$ for $n\ge 2$.

Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a…

We show how the Gelfand spectrum of certain commutative operator algebras can be studied based on the theorem of Stone and von Neumann. The method presented is a natural addition to the tools of quantum spectral synthesis, which were…

We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra $\mathfrak{g}$ are Noetherian rings and finitely generated rings over $\mathbb{C}(q)$. Moreover, we…

By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $SU_q(N)$ quantum algebra by means of a…

We undertake a systematic study of the so-called $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$. This is the universal $C^*$-algebra generated by a unitary $U$ and an isometry $S_2$ such that $S_2U=U^2S_2$ and $S_2S_2^*+US_2S_2^*U^*=1$.…

This paper brings together C*-algebras and algebraic topology in terms of viewing a C*-algebraic invariant in terms of a topological spectrum. E-theory, E(A,B), is a bivariant functor in the sense that is a cohomology functor in the first…

The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present contribution,…

Representing Z/N as roots of unity, we restrict a natural U(1)-action on the Heegaard quantum sphere to Z/N, and call the quotient spaces Heegaard quantum lens spaces. Then we use this representation of Z/N to construct an associated…

Let $M$ be a compact oriented $d$-dimensional smooth manifold. Chas and Sullivan have defined a structure of Batalin-Vilkovisky algebra on $\mathbb{H}_*(LM)$. Extending work of Cohen, Jones and Yan, we compute this Batalin-Vilkovisky…

We say that a $C^*$-algebra $\mathcal{A}$ satisfies the similarity property ((SP)) if every bounded homomorphism $u\colon \mathcal{A} \to \mathcal{B}(\mathit{H})$, where $\mathit{H}$ is a Hilbert space, is similar to a $*$-homomorphism. We…

This paper examines the relationship between certain non-commutative analogues of projective 3-space, $\mathbb{P}^3$, and the quantized enveloping algebras $U_q(\mathfrak{sl}_2)$. The relationship is mediated by certain non-commutative…

We show that the representation category of the quantum group of a non-degenerate bilinear form is monoidally equivalent to the representation category of the quantum group SL_q(2), for a well chosen non-zero parameter q. The main…

we study the exponential map for A_n = R^2^n, the Cayley_Dickson algebras for n bigher than 1,wich generalize the Complex exponential map to Quaternions,Octonions and so forth. As application,we show that the self-map of the unit sphere in…

We introduce the notions of Hopf quasigroup and Hopf coquasigroup $H$ generalising the classical notion of an inverse property quasigroup $G$ expressed respectively as a quasigroup algebra $k G$ and an algebraic quasigroup $k[G]$. We prove…