Research
Research
Research
Research
10,089+ 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…
We study scale-invariant geometric quantities associated with embedded closed curves in Euclidean three-space, with an emphasis on their behavior under optimization within a fixed knot type. Given a E…
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…
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…
We show that under $\mathsf{ZF} + \mathsf{CC}_{\mathbb R}$, if the Ramsey property holds for all sets in a good pointclass $\Gamma$, then there is no MAD family in $\Gamma$, proving a long-standing co…
Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…
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…
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 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}}…
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…
We construct families of $k$-step nilpotent symplectic Lie algebras associated with graphs, extending the construction given in [Pouseele-Tirao, JPAA 213 (2009)] for the 2-step case. We also show th…
We study the nonlinear generalized heat equation $C(u)u_t=\frac{1}{z^{\nu}}\left(K(u)z^{\nu}u_z\right)_z$, where $C(u)$ and $K(u)$ are temperature-dependent thermal coefficients and $\nu>0$ is a geome…
We study a family of scale-invariant $p$-densities of knot types in $R^3$, defined as the ratio of length to an $L^p$-type spread of pairwise distances along a curve. The first point of the paper is t…
Let $A:=\mathbb{C}[z_+,z_-]\otimes \Lambda(\theta_1,\theta_2,\theta_3)$, with $z_\pm$ even and $\theta_1,\theta_2,\theta_3$ odd. For a reductive Lie algebra $\mathfrak g$, let $\mathfrak g[A]:=\mathfr…
In this paper, we obtain a weighted trigonometric summation formula which is an extension of the trigonometric summation formula by Grigor'yan, Lin and Yau \cite{GLY}.…
We establish the existence and uniqueness of discrete Einstein metrics on trees under Lin-Lu-Yau Ricci curvature using Perron-Frobenius theory. Notably, the existence of a positive-curvature Einstein …
We introduce multiplicative Ehresmann connections on surjective submersions of Lie groupoids, extending both the classical notion of Ehresmann connections on fibre bundles and the more recent notion o…
We study simplicity of Lie skew braces from both global and infinitesimal perspectives. After reviewing the correspondence between connected Lie skew braces, simply transitive affine actions, and post…
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