Results 41 to 50 of about 579 (182)
Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
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On a generalization of clifford algebras
Journal of Algebra, 1971 Let V be a vector space over a field k, Q a quadratic form on V, T(V) the tensor algebra of IT. We want to study those algebras C generated by 77 having the following property(P)? Any isometry on Vwith respect to Q can be extended to an automorphism of C having invariant V, and conversely, every automorphism of C mapping V onto itself induces an ...
openaire +2 more sources
Efficient Gaussian Simulations of Fermionic Open Quantum Systems
Advanced Quantum Technologies, Volume 9, Issue 4, April 2026.Building upon Bravyi's fundamental theoretical framework, efficient classical simulation methods are reviewed and further developed for general fermionic Gaussian processes. The emphasis remains on a unified approach applicable to generic fermionic Gaussian operations.
Yinan Fang +3 more
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Special Vinberg cones of rank 4
Journal of High Energy PhysicsE.B. Vinberg developed a theory of homogeneous convex cones $$C\subset V={\mathbb{R}}^{n}$$ , which has many applications. He gave a construction of such cones in terms of non-associative rank n matrix T-algebras $$\mathcal{T}$$ , that consist of vector ...
D. V. Alekseevsky, P. Osipov
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On the Geometric Structure of Hyperbolic Clifford Bundles and Associated Spin Groups
AxiomsIn this paper, we present the spinor structure associated with the Hyperbolic Clifford algebra of a real n-dimensional vector space V, which is denoted by ClHV.
Eduardo Notte-Cuello
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Noncommutative polygonal cluster algebras
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg +3 more
wiley +1 more source
Operator Homology and Cohomology in Clifford Algebras
Cubo, 2010 In recent work, the authors used canonical lowering and raising operators to define Appell systems on Clifford algebras of arbitrary signature. Appell systems can be interpreted as polynomial solutions of generalized heat equations, and in probability ...
René Schott, G. Stacey Staples
doaj
Causal analysis of extreme risk in a network of industry portfolios
Canadian Journal of Statistics, Volume 54, Issue 1, March 2026.Abstract We provide a detailed review of causal dependence within the framework of max‐linear structural models. Such models express each node variable as a max‐linear function of its parental node variables in a directed acyclic graph (DAG) and some exogenous innovation.
Claudia Klüppelberg, Mario Krali
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Analyzing the Free States of one Quantum Resource Theory as Resource States of Another
Advanced Quantum Technologies, Volume 9, Issue 2, February 2026.The article investigates how free states in one quantum resource theory can become highly resourceful in another. It systematically studies multipartite entanglement, fermionic non‐Gaussianity, imaginarity, realness, spin coherence, Clifford non‐stabilizerness, Sn‐equivariance, and non‐uniform entanglement, combining rigorous analytical tools and ...
Andrew E. Deneris +5 more
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Derangements in intransitive groups
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract Let G$G$ be a nontrivial permutation group of degree n$n$. If G$G$ is transitive, then a theorem of Jordan states that G$G$ has a derangement. Equivalently, a finite group is never the union of conjugates of a proper subgroup. If G$G$ is intransitive, then G$G$ may fail to have a derangement, and this can happen even if G$G$ has only two ...
David Ellis, Scott Harper
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