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Homomorphism Tensors and Linear Equations
[article]
2022
arXiv
pre-print
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The existence of certain linear transformations between such homomorphism tensor subspaces can be interpreted both as homomorphism indistinguishability over a graph class and as feasibility of an equational ...
In this paper, we provide a unified algebraic framework for such results by examining the linear-algebraic and representation-theoretic structure of tensors counting homomorphisms from labelled graphs. ...
Homomorphism Tensors and Homomorphism Tensor Maps. ...
arXiv:2111.11313v2
fatcat:7xwmantsajayxivhhel5avf2we
Page 109 of Mathematical Reviews Vol. 7, Issue 3
[page]
1946
Mathematical Reviews
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amounts e¢; (when all ¢; are zero we have the special case of linear equations). ...
Thus the theory of functors is also applicable to abstract sets, linear spaces, and so on. In the case of groups, mappings are understood to be homomorphisms. ...
Tensors as module homomorphisms over group rings
[article]
2010
arXiv
pre-print
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Braman [B08] described a construction where third-order tensors are exactly the set of linear transformations acting on the set of matrices with vectors as scalars. ...
Our generalization allows for any abelian group to replace the cyclic group, any commutative ring with identity to replace the field of real numbers, and an arbitrary order tensor to replace third-order ...
Moreover, any third-order tensor is a linear transformation over this module and any linear transformation over the module can be represented as a third-order tensor. ...
arXiv:1005.1894v1
fatcat:l7kawcrtszezhalmpca4o5fytu
Page 674 of Mathematical Reviews Vol. , Issue 93b
[page]
1993
Mathematical Reviews
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Barvinok (S-RIT)
15 LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY
93b:15034 Li, Jian Xin A new algorithm for the greatest solution of fuzzy bilinear equations. ...
Fuzzy Sets and Systems 46 (1992), no. 2, 193-210.
From the summary: “The equations A,;x = A2x are called fuzzy bilinear equations. In this paper, we define the extended fuzzy bilinear equations x! ...
Algebraic Reductions of Knowledge
[article]
2022
IACR Cryptology ePrint Archive
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We construct and study the tensor reduction, which is capable of reducing any homomorphic statement composed via the tensor product, and provides knowledge soundness unconditionally when working over vector ...
We additionally show that tensor reductions can be employed to construct reductions of knowledge with logarithmic communication for familiar linear algebraic statements, and in turn, these can be composed ...
Equation (18), the prover and verifier run a reduction of knowledge for linear forms. ...
dblp:journals/iacr/KothapalliP22
fatcat:b2msxt5nb5ck7my4l7qz5pvuoe
Conformal linear gravity in de Sitter space
2010
Journal of Mathematical Physics
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2009 pre-print arXiv:0903.5249v1 fatcat:ypbhxgwyfzcdbbe36aeblkujrmOther Versions
It has been shown that the theory of linear conformal quantum gravity must include a tensor field of rank-3 and mixed symmetry [1]. ...
Then, in order to relate this field with the symmetric tensor field of rank-2, _αβ related to graviton, we will define homomorphisms between them. ...
As a future work, it may be possible to find a CI gravitational field which in its linear approximation gives this linear physical equation. ...
doi:10.1063/1.3321581
fatcat:u3bugpjlyzhafowwj2ukgqzltq
Differential Operators Preserving Relations of Automorphy
1963
Transactions of the American Mathematical Society
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A holomorphic differential %^-homomorphism 2 of order 1 is a dè-homomorphism if and only if:
formula (2.10) of Theorem 1, the right-hand side R of equation (4.7) can be written as Vij(zaczbd) -(2.10) ...
) in [6]), and solving the resulting set of linear equations in c,c1,c2,c3.Since this is a straightforward calculation, the details will be omitted, except for the following observation. ...
doi:10.2307/1993611
fatcat:mnuqryo7ubczrk7z2amryx5e4i
Differential operators preserving relations of automorphy
1963
Transactions of the American Mathematical Society
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A holomorphic differential %^-homomorphism 2 of order 1 is a dè-homomorphism if and only if:
formula (2.10) of Theorem 1, the right-hand side R of equation (4.7) can be written as Vij(zaczbd) -(2.10) ...
) in [6]), and solving the resulting set of linear equations in c,c1,c2,c3.Since this is a straightforward calculation, the details will be omitted, except for the following observation. ...
doi:10.1090/s0002-9947-1963-0168803-0
fatcat:eu73qyzi25ei7fxivceycktwiy
On universal solution to reflection equation
[article]
2002
arXiv
pre-print
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We introduce universal solution to the reflection equation (RE) and deduce a fusion prescription for RE-matrices ...
We show that the braided bialgebra structure of ^* is naturally described by means of twisted tensor powers of and their module algebras. ...
It will satisfy equations (25) and (26) in B ⊗ B ⊗B * . ...
arXiv:math/0210242v1
fatcat:d4vxv57dfbgbnmgjuu7ha7thqm
Contents
[chapter]
2022
Abstract Algebra
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of equations by radicals | 280 Group actions | 86 Orbits and stabilizers | 89 12.5 Roots of Polynomials and Discriminants | 288 5.3 13 Applications to the structure of groups | 93 Tensor Products | 292 ...
8.2 Linear independence, basis and dimension | 148 8.3 Linear mappings | 158 8.4 Eigenvalues and eigenvectors | 167 9 Introduction to Modules | 180 9.1 Elements of module theory | 180 9.2 Modules over ...
doi:10.1515/9783110691160-toc
fatcat:7wqnwsd6dned7jpyqnoo5fuxv4
Sofic Lie Algebras
[article]
2022
arXiv
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We introduce and study soficity for Lie algebras, modelled after linear soficity in associative algebras. ...
Finally, we give explicit families of almost representations for the Witt and Virasoro algebras. ...
The lemma show that SR(L) = Θ∈S ker Θ where S = Θ : L → ω gl n k (F )/ρ ω | Θ is a Lie algebra homomorphism
Tensor each component of Ψ m with an appropriately sized identity matrix gives us maps Ψm : ...
arXiv:2202.13025v3
fatcat:2ww65fdvzfev3hpblmzlynntbe
WIGNER–ECKART THEOREM FOR TENSOR OPERATORS OF HOPF ALGEBRAS
2005
International Journal of Geometric Methods in Modern Physics (IJGMMP)
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2004 pre-print arXiv:math-ph/0404019v1 fatcat:2ifk7tomhzexrfm4kytxz4mx7i
We prove Wigner-Eckart theorem for the irreducible tensor operators for arbitrary Hopf algebras, provided that tensor product of their irreducible representation is completely reducible. ...
Two classes of tensor operators for the Hopf algebra U_t(su(2)) are considered. The reduced matrix elements for the class of irreducible tensor operators are calculated. ...
The linear mapping f ∈ Hom(V, W ) is a homomorphism of representations if and only if f is an invariant element of the representation (Hom(V, W ), δ). ...
doi:10.1142/s0219887805000594
fatcat:ghjkfx446zdflecr4z6yomb7iq
A Conformal Wave Equation
1935
Proceedings of the National Academy of Sciences of the United States of America
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The wave equation which we are seeking should be a linear combination of these covariant derivatives with appropriate matrices as coefficients. ...
Thus, when dealing with a homology theory involving a direct homomorphism sequence, the integers form the natural coefficient group; and, when dealing with a homology theory involving an inverse homomorphism ...
doi:10.1073/pnas.21.7.484
pmid:16588007
pmcid:PMC1076633
fatcat:er6gsrjxyngm7kw4auzxouvb3e
Page 5086 of Mathematical Reviews Vol. , Issue 82m
[page]
1982
Mathematical Reviews
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The main results concern relations between solutions of a pair of tensor products of systems of linear homogeneous inequalities and solutions of tensor factor systems of matrix equations and vice versa ...
matrices A and B to establish some relationships between tensor factor systems of linear homogeneous inequalities and tensor products of matrices. ...
Multilinear Algebras and Tensors with Vector Subbundle of Manifolds
2015
Dhaka University Journal of Science
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A Theorem 1.32. is established by using sections and fibrewise orthogonal sections of an application of Gran-Schmidt. ...
In the present paper some aspects of tensor algebra, tensor product, exterior algebra, symmetric algebra, module of section, graded algebra, vector subbundle are studied. ...
Finally, this induced homomorphism makes a covariant function from the category of −modules −linear maps to the category of graded algebras over and graded algebra homomorphisms. Definition 1.16. ...
doi:10.3329/dujs.v62i1.21957
fatcat:xed2xez5jzc7llmldny6r7fhvm
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