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Homomorphism Tensors and Linear Equations
[article]

2022
*
arXiv
*
pre-print

The existence of certain

arXiv:2111.11313v2
fatcat:7xwmantsajayxivhhel5avf2we
*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. ...##
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Page 109 of Mathematical Reviews Vol. 7, Issue 3
[page]

1946
*
Mathematical Reviews
*

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*. ...##
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Tensors as module homomorphisms over group rings
[article]

2010
*
arXiv
*
pre-print

Braman [B08] described a construction where third-order

arXiv:1005.1894v1
fatcat:l7kawcrtszezhalmpca4o5fytu
*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*. ...##
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Page 674 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

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! ...##
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Algebraic Reductions of Knowledge
[article]

2022
*
IACR Cryptology ePrint Archive
*

We construct

dblp:journals/iacr/KothapalliP22
fatcat:b2msxt5nb5ck7my4l7qz5pvuoe
*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. ...##
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Conformal linear gravity in de Sitter space

2010
*
Journal of Mathematical Physics
*

It has been shown that the theory of

doi:10.1063/1.3321581
fatcat:u3bugpjlyzhafowwj2ukgqzltq
*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*. ...##
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Differential Operators Preserving Relations of Automorphy

1963
*
Transactions of the American Mathematical Society
*

A holomorphic differential %^-

doi:10.2307/1993611
fatcat:mnuqryo7ubczrk7z2amryx5e4i
*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. ...##
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Differential operators preserving relations of automorphy

1963
*
Transactions of the American Mathematical Society
*

A holomorphic differential %^-

doi:10.1090/s0002-9947-1963-0168803-0
fatcat:eu73qyzi25ei7fxivceycktwiy
*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. ...##
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On universal solution to reflection equation
[article]

2002
*
arXiv
*
pre-print

We introduce universal solution to the reflection

arXiv:math/0210242v1
fatcat:d4vxv57dfbgbnmgjuu7ha7thqm
*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 * . ...##
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Contents
[chapter]

2022
*
Abstract Algebra
*

of

doi:10.1515/9783110691160-toc
fatcat:7wqnwsd6dned7jpyqnoo5fuxv4
*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 ...##
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Sofic Lie Algebras
[article]

2022
*
arXiv
*
pre-print

We introduce

arXiv:2202.13025v3
fatcat:2ww65fdvzfev3hpblmzlynntbe
*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 : ...##
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WIGNER–ECKART THEOREM FOR TENSOR OPERATORS OF HOPF ALGEBRAS

2005
*
International Journal of Geometric Methods in Modern Physics (IJGMMP)
*

We prove Wigner-Eckart theorem for the irreducible

doi:10.1142/s0219887805000594
fatcat:ghjkfx446zdflecr4z6yomb7iq
*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). ...##
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A Conformal Wave Equation

1935
*
Proceedings of the National Academy of Sciences of the United States of America
*

The wave

doi:10.1073/pnas.21.7.484
pmid:16588007
pmcid:PMC1076633
fatcat:er6gsrjxyngm7kw4auzxouvb3e
*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*...##
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Page 5086 of Mathematical Reviews Vol. , Issue 82m
[page]

1982
*
Mathematical Reviews
*

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. ...##
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Multilinear Algebras and Tensors with Vector Subbundle of Manifolds

2015
*
Dhaka University Journal of Science
*

A Theorem 1.32. is established by using sections

doi:10.3329/dujs.v62i1.21957
fatcat:xed2xez5jzc7llmldny6r7fhvm
*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. ...
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