On matrices in prescribed conjugacy classes with no common invariant subspace and sum zero

Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity

We study the possible dimension vectors of indecomposable parabolic bundles on the projective line, and use our answer to solve the problem of characterizing those collections of conjugacy classes of n by n matrices for which one can find matrices in their closures whose product is equal to the identity matrix. Both answers depend on the root system of a Kac-Moody Lie algebra. Our proofs use Ringel's theory of tubular algebras, work of Mihai on the existence of logarithmic connections, the Riemann-Hilbert correspondence and an algebraic version, due to Dettweiler and Reiter, of Katz's middle c…

余模范畴中的指定对偶动力学

Prescribed duality dynamics in comodule categories

该研究构造出对极满而非双射且无来自双射对极Hopf代数非平凡同态的Hopf代数，解决了公开问题，并通过实现指定子空间格为余模格的现象给出构造，揭示了Hopf代数对极性质的对偶不对称性。

A different perspective on H-like Lie algebras

We characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in $\mathfrak{so}(\mathbb{R}^q)$, translating the classification problem for H-like Lie algebras to an equivalent problem in linear algebra. We study properties of H-like Lie algebras, present new methods for constructing them, including tensor products and central sums, and classify H-like Lie algebras whose associated $J_Z$-maps have rank two for all nonzero $Z$.

奇特征有限域上正交空间生成的压缩感知矩阵

Compressed sensing matrices from orthogonal spaces over finite fields of odd characteristic

本文从奇特征有限域正交空间子空间构造确定性压缩感知矩阵，建立其满足受限等距性质的充分条件，通过与DeVore构造对比说明相关性能权衡。