Results 41 to 50 of about 596 (183)
Theorem on the norm of elements of spinor groups
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2011 In this article we consider Clifford's algebra over the field of real numbers of finite dimension. We define the operation of Hermitian conjugation for the elements of Clifford's algebra.
Dmitry S Shirokov
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Fortschritte der Physik, Volume 74, Issue 5, May 2026.ABSTRACT We provide full details of a BV formulation of N=1$\mathcal N=1$ supergravity in 10 dimensions, to all orders in fermions, built from the generalised geometry description of the theory. In contrast to standard treatments, we introduce neither the degrees of freedom corresponding to orthonormal frames for the metric nor the local Lorentz ...
Julian Kupka +2 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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Deforming the Double‐Scaled SYK and Reaching the Stretched Horizon From Finite Cutoff Holography
Fortschritte der Physik, Volume 74, Issue 5, May 2026.ABSTRACT We study the properties of the double‐scaled SYK (DSSYK) model under chord Hamiltonian deformations based on finite cutoff holography for general dilaton gravity theories with Dirichlet boundaries. The formalism immediately incorporates a lower‐dimensional analog of TT¯(+Λ2)$\text{T}\overline{\text{T}}(+\Lambda _2)$ deformations, denoted T2 ...
Sergio E. Aguilar‐Gutierrez
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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
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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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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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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 ...
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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
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