Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks

We construct nonassociative quasi-stationary solutions describing deformations of Schwarzschild black holes, BHs, to ellipsoid configurations, which can be black ellipsoids, BEs, and/or BHs with ellipsoidal accretion disks. Such solutions are defined by generic off-diagonal symmetric metrics and nonsymmetric components of metrics (which are zero on base four dimensional, 4-d, Lorentz manifold spacetimes but nontrivial in respective 8-d total (co) tangent bundles). Distorted nonassociative BH and BE solutions are found for effective real sources with terms proportional to $$\hbar \kappa $$ ħ κ (for respective Planck and string constants). These sources and related effective nontrivial cosmological constants are determined by nonlinear symmetries and deformations of the Ricci tensor by nonholonomic star products encoding R-flux contributions from string theory. To generate various classes of (non) associative /commutative distorted solutions we generalize and apply the anholonomic frame and connection deformation method for constructing exact and parametric solutions in modified gravity and/or general relativity theories. We study properties of locally anisotropic relativistic, optically thick, could and thin accretion disks around nonassociative distorted BHs, or BEs, when the effects due to the rotation are negligible. Such configurations describe angular anisotropic deformations of axially symmetric astrophysical models when the nonassociative distortions are related to the outer parts of the accretion disks.

Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra

We consider a class of exponentials in the Weyl-Heisenberg algebra with exponents of type at most linear in coordinates and arbitrary functions of momenta. They are expressed in terms of normal ordering where coordinates stand to the left from momenta. Exponents appearing in normal ordered form satisfy differential equations with boundary conditions that could be solved perturbatively order by order. Two propositions are presented for the Weyl-Heisenberg algebra in 2 dimensions and their generalizations in higher dimensions. These results can be applied to arbitrary noncommutative spaces for construction of star products, coproducts of momenta and twist operators. They can also be related to the BCH formula.

Wick rotations in deformation quantization

We study formal and non-formal deformation quantizations of a family of manifolds that can be obtained by phase space reduction from [Formula: see text] with the Wick star product in arbitrary signature. Two special cases of such manifolds are the complex projective space [Formula: see text] and the complex hyperbolic disc [Formula: see text]. We generalize several older results to this setting: The construction of formal star products and their explicit description by bidifferential operators, the existence of a convergent subalgebra of “polynomial” functions, and its completion to an algebra of certain analytic functions that allow an easy characterization via their holomorphic extensions. Moreover, we find an isomorphism between the non-formal deformation quantizations for different signatures, linking, e.g., the star products on [Formula: see text] and [Formula: see text]. More precisely, we describe an isomorphism between the (polynomial or analytic) function algebras that is compatible with Poisson brackets and the convergent star products. This isomorphism is essentially given by Wick rotation, i.e. holomorphic extension of analytic functions and restriction to a new domain. It is not compatible with the [Formula: see text]-involution of pointwise complex conjugation.

Defining relations of quantum symmetric pair coideal subalgebras

We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras of quantised enveloping algebras of Kac–Moody type. Our methods are based on star products on noncommutative ${\mathbb N}$ -graded algebras. The resulting defining relations are expressed in terms of continuous q-Hermite polynomials and a new family of deformed Chebyshev polynomials.

Bivariate continuous q-Hermite polynomials and deformed quantum Serre relations

We introduce bivariate versions of the continuous [Formula: see text]-Hermite polynomials. We obtain algebraic properties for them (generating function, explicit expressions in terms of the univariate ones, backward difference equations and recurrence relations) and analytic properties (determining the orthogonality measure). We find a direct link between bivariate continuous [Formula: see text]-Hermite polynomials and the star product method of [S. Kolb and M. Yakimov, Symmetric pairs for Nichols algebras of diagonal type via star products, Adv. Math. 365 (2020), Article ID: 107042, 69 pp.] for quantum symmetric pairs to establish deformed quantum Serre relations for quasi-split quantum symmetric pairs of Kac–Moody type. We prove that these defining relations are obtained from the usual quantum Serre relations by replacing all monomials by multivariate orthogonal polynomials.

Value of High-Quality Logistics: Evidence from a Clash Between SF Express and Alibaba

Consumers regard product delivery as an important service component that influences their shopping decisions on online retail platforms. Delivering products to customers in a timely and reliable manner enhances customer experience and companies’ profitability. In this research, we explore the extent to which customers value a high-quality delivery experience when shopping online. Our identification strategy exploits a natural experiment: a clash between SF Express and Alibaba, the largest private logistics service provider with the highest reputation in delivery quality in China and the largest online retail platform in China, respectively. The clash resulted in Alibaba unexpectedly removing SF Express as a shipping option from Alibaba’s retail platform for 42 hours in June 2017. Using a difference-in-differences design, we analyze the market performance of 129,448 representative stock-keeping units on Alibaba to quantify the economic value of a high-quality delivery service to sales, product variety, and logistics rating. We find that the removal of the high-quality delivery option from Alibaba’s retail platform reduced sales by 14.56% during the clash, increased the contribution of long-tail to total sales—sales dispersion—by 3%, but did not impact the variety and logistics rating of sold products. Furthermore, we also identify product characteristics that attenuate the value of high-quality logistics and find that the removal of SF Express is more obstructive for (1) star products as compared with long-tail products because the same star products are likely to be supplied by competing retail platforms that customers can easily switch to, (2) expensive products because customers need a reliable delivery service to protect their valuable items from damage or loss, and (3) less-discounted products because customers are more willing to sacrifice the service quality over a price markdown. This paper was accepted by Victor Martínez-de-Albéniz, operations management.