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Research
Research
16,379+ open-access research outputs.
In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is s…
There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this paper, we extend suc…
Let $F$ be a finite field of odd characteristic. We prove that any set $A\subset F$ with $|A|\geq C|F|^{5/6}$ contains a nontrivial quadratic progression $(x, x+y, x+y^2), y\neq 0.$ For prime fields, …
We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to …
In this paper, we utilize our previous results on mod p monodromy of cyclic coverings of the projective line to realize a large series of groups of the form PSL(n, q) and PSU(n, q) as Galois groups ov…
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
Skin lesion classification is essential for early dermatological diagnosis, yet many existing computer-aided systems rely primarily on dermoscopic images and underutilize the multimodal evidence routi…
As healthcare systems become increasingly interconnected, ensuring secure and continuous device authentication in health information exchange (HIE) networks is critical to safeguarding patient data an…
In this paper, we investigate non-abelian extensions of Lie algebras with derivations using several different approaches. We show that the theory of non-abelian extensions of a Lie algebra with a deri…
Given a holomorphic Lie algebroid $(V, \phi)$ on a compact connected Riemann surface $X$, we give a necessary and sufficient condition for a parabolic vector bundle on $X$, with parabolic structure ov…
All current LLM serving systems place the GPU at the center, from production-level attention-FFN disaggregation to NVIDIA's Rubin GPU-LPU heterogeneous platform. Even academic PIM/PNM proposals still …
The Quantum Approximate Optimization Algorithm (QAOA) follows a single, fixed evolution path, overlooking the potential computational advantage of coherently superposing multiple trajectories. Here we…
In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the categ…
We present a criterion that serves as the basis for a polynomial-time algorithm to decide whether a finite set of qudit gates exponentiated by some Hamiltonians is universal. Our approach formulates u…
We characterise the existence of balanced and pluriclosed metrics on compact quotients of real semisimple Lie groups equipped with regular complex structures, in terms of Vogan diagrams. Consequently,…
Let $\bar{S}_2$ be the Lie algebra of polynomial vector fields on $A_2=\mathbb{C}[t_1,t_2]$ with constant divergence.In this paper, we first show that each block $\Omega^{\widetilde{S}_2}_{\mathbf{a}}…
Time-fractional telegraph equations provide fundamental mathematical models for transport processes that exhibit memory and nonlocal effects in industrial and physical systems. These models arise natu…
We develop a Koszul-theoretic framework for comparing classical Alexander-type invariants with infinitesimal invariants arising from finite-type commutative differential graded algebra models. The cen…
In this article, we introduce a time-independent version of the L\'evy colored noise considered in Balan (2015) and Balan and Jim\'enez (2026). We study the existence of the solution of a linear stoch…
We present a framework for non-Abelian p-loop, fracton, and planon condensation in 3+1 dimensions by constructing extended cage-net fracton models using decoupled layers of the Hu-Geer-Wu (HGW) string…
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