We provide a quiver setting for quasi-Hopf algebras, generalizing the Hopf quiver theory. As applications we obtain some general structure theorems, in particular the quasi-Hopf analogue of the Cartier theorem and the Cartier-Gabriel decomposition theorem.

In this paper we present an alternative proof for the existence theorem of the singular value decomposition in the extended max algebra and we propose some possible extensions of the max-algebraic singular value decomposition. We also prove the existence of a kind of QR decomposition in the extended max algebra.

In this paper we present a decomposition theorem for hermitian forms over fields of characteristic 2 refining the usual Witt decomposition in this case. We apply this decomposition to algebras with involution over fields of characteristic 2 to give a complete description of the effect of passing to a generic splitting field of the algebra on the isotropy of the involution.

In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed ‘Herman map’ is developed. It’s shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations an...

An exact manifold with pseudoconvex boundary (PC manifold, for short) is a compact complex manifold X, which admits a strictly pluri-subharmonic Morse function ψ, such that the set of maximum points of ψ coincides with the boundary ∂X. We prefer the term PC manifold, since the combination of words “compact Stein manifold” is likely to precipitate heart palpitations in some mathematicians. Such ...

This expository paper is intended for a short self-contained introduction to the theory of infinite convolutions probability measures on Polish semigroups. We give proofs Rees decomposition theorem completely simple semigroups, Ellis–Żelazko theorem, convolution factorization idempotents, and cluster points convolutions.

Haghverdi introduced the notion of unique decomposition categories as a foundation for categorical study of Girard’s Geometry of Interaction (GoI). The execution formula in GoI provides a semantics of cut-elimination process, and we can capture the execution formula in every unique decomposition category: each hom-set of a unique decomposition category comes equipped with a partially defined co...

Here we briefly sketch the original proof of [BBD]. The main reference of this talk would be [dCM1], the expository article for this subject written by de Cataldo and Migliorini. The main idea of [BBD] is that first we prove this theorem over a finite field and use ”spread out” principle. One of the important property of this method is that we have an action of the Galois group which acts on va...

The Jordan decomposition states that a function f : R → R is of bounded variation if and only if it can be written as the difference of two monotone increasing functions. In this paper we generalize this property to real valued BV functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A...