相关论文: Products, coproducts and singular value decomposit…
This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.
A special subcomplex of the singular chain complex for a topological space, historically called oriented singular chain complex is used here with the new name "alternative" singular chain complex. It was already known that this subcomplex…
In signal processing and identification, generalized singular value decomposition (GSVD), related to a sequence of matrices in product/quotient form are essential numerical linear algebra tools. On behalf of the growing demand for efficient…
Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions to finite complexes of real vector spaces. We provide two…
We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…
We provide a unified treatment of several commuting tensor products considered in the literature, including the tensor product of enriched categories and the Boardman-Vogt tensor product of operads and symmetric multicategories, subsuming…
In singular value decomposition (SVD) of a complex matrix A, the singular vectors or the eigenvectors of AA{\dag} and A{\dag}A are unique up to complex phase factors. Thus, the two unitary matrices in SVD are unique up to diagonal matrices…
We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton…
In this article, we consider tensor products of unitary representations by irreducible non-unitary finite dimensional representations of topological groups to define a property that is a twisting of Kazhdan's Property (T). We use the…
This is a note for constructing fundamental invariants and computing the Hilbert series of the invariant subalgebras of tensor products of polynomial rings under the action by a direct product of symmetric groups. Our computation relies on…
A non-unital algebra in a closed monoidal category is called self-induced if the multiplication induces an isomorphism between A\otimes_A A and A. For such an algebra, we define smoothening and roughening functors that retract the category…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this result to prove generalizations and variants of the Steinberg…
We consider generic degenerate subvarieties $X_i\subset\mathbb{P}^n$. We determine an integer $N$, depending on the varieties, and for $n\geq N$ we compute dimension and degree formulas for the Hadamard product of the varieties $X_i$.…
Connectivity is a homotopy invariant property of a separable C*-algebra A which has three important consequences: absence of nontrivial projections, quasidiagonality and realization of the Kasparov group KK(A,B) as homotopy classes of…
In [8], Arveson proved that a $1$-parameter decomposable product system is isomorphic to the product system of a CCR flow. We show that the structure of a generic decomposable product system, over higher dimensional cones, modulo twists by…
We study the general form of the noncommutative associative product (the star-product) on the Grassman algebra; the star-product is treated as a deformation of the usual "pointwise" product. We show that up to a similarity transformation,…
A polyhedral product is a natural subspace of a Cartesian product, which is specified by a simplicial complex K. The automorphism group Aut(K) of K induces a group action on the polyhedral product. In this paper we study this group action…
We say that an algebra is zero-product balanced if $ab\otimes c$ and $a\otimes bc$ agree modulo tensors of elements with zero-product. This is closely related to but more general than the notion of a zero-product determined algebra of…
We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence…