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Adding homomorphisms to commutative/monoidal theories or how algebra can help in equational unification
[chapter]

1991
*
Lecture Notes in Computer Science
*

The class encompasses important examples like the theories

doi:10.1007/3-540-53904-2_91
fatcat:6jzlkhtkxnccfmbmwzr3xccnra
*of**abelian*monoids , idempotent*abelian*monoids , and*abelian**groups*. ... The*two*results illustrate how using algebraic machinery can lead to general results and elegant proofs*in**unification*theory. ... Well-known examples*of*commutative theories are the theory AM*of**abelian*monoids, the theory AIM*of*idempotent*abelian*monoids (sometimes called AC1*in*the literature), and the theory AG*of**abelian**groups*...##
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Page 162 of Proceedings of the National Academy of Sciences of the United States of America Vol. 21, Issue 3
[page]

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

It is through the study

*of*rings*in*general and perhaps also*semi*-rings that we may expect a*unification**of*the*two*subjects. ... This form*of*definition immediately suggests the generalization obtained by replacing the words ‘‘*Abelian**group*” by ‘‘*semi*-*group*”*in*the above. ...##
###
Page 7646 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

*of*

*two*

*terms*

*in*

*abelian*

*groups*. ... Lett. 52 (1994), no.2, 61-68. 95m:68020b 68N15 Rittri, Mikael (S-CHAL-C; Goteborg) Corrigendum: “

*Semi*-

*unification*

*of*

*two*

*terms*

*in*

*abelian*

*groups*”. Inform. Process. Lett. 53 (1995), no.4, 235. ...

##
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A Twist on Broken U(3)xU(3) Supersymmetry
[article]

2021
*
arXiv
*
pre-print

Starting with a supersymmetric SU(3)xSU(3)xU(1)xU(1) gauge theory, the 18 adjoint-representation gauginos are replaced with 2 families

arXiv:1911.04593v4
fatcat:onqkz4xsqfgszaosf6klukahxu
*of*9 gauginos*in*the (3,3*) representation*of*the*group*. ... After this explicit breaking*of*supersymmetry,*two*-loop quadratic divergences still cancel at a*unification*scale. ...*In*addition, four more chiral multiplets are added:*two*transform*in*the adjoint+singlet representations*of*the*two*SU(3)*groups*. ...##
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Homogeneous Equations of Algebraic Petri Nets
[article]

2016
*
arXiv
*
pre-print

One way to specify correctness

arXiv:1606.05490v3
fatcat:doq5fctxejdxhf4keed34nmngy
*of*an algebraic Petri net model N is to specify a linear equation E over the places*of*N based on*term*substitution, and coefficients from an*abelian**group*G. ...*In*this paper, we provide a complete characterization*of*stability for the subclass*of*homogeneous linear equations, by restricting ourselves to the interpretation*of**terms*over the Herbrand structure ... We lift substitutions from*terms*to polynomials over*terms*and*abelian**groups*by pointwise substitution and subsequent "simplification"*of*the polynomial: ▸ Definition 10 (Substitutions*in*Polynomials ...##
###
Homogeneous Equations of Algebraic Petri Nets

2016
*
International Conference on Concurrency Theory
*

One way to specify correctness

doi:10.4230/lipics.concur.2016.14
dblp:conf/concur/TriebelS16
fatcat:hvsqmznhtngpxalnce5wvjz4zi
*of*an algebraic Petri net model N is to specify a linear equation E over the places*of*N based on*term*substitution, and coefficients from an*abelian**group*G. ...*In*this paper, we provide a complete characterization*of*stability for the subclass*of*homogeneous linear equations, by restricting ourselves to the interpretation*of**terms*over the Herbrand structure ... We lift substitutions from*terms*to polynomials over*terms*and*abelian**groups*by pointwise substitution and subsequent "simplification"*of*the polynomial: ▸ Definition 10 (Substitutions*in*Polynomials ...##
###
Unification mechanism for gauge and spacetime symmetries

2017
*
Journal of Physics A: Mathematical and Theoretical
*

A

doi:10.1088/1751-8121/aa5c04
fatcat:lldkkynrrnd5xgudvjgtcaw2ui
*group*theoretical mechanism for*unification**of*local gauge and spacetime symmetries is introduced. ... theorems*in*a non-supersymmetric way. ...*in**terms**of**two*-spinors. ...##
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Theories of Homomorphic Encryption, Unification, and the Finite Variant Property

2014
*
Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming - PPDP '14
*

an

doi:10.1145/2643135.2643154
dblp:conf/ppdp/YangEMMN14
fatcat:ss5awwz6wffnnlp6i67rg5svcu
*Abelian**group*. ...*In*this paper we address this problem by studying various approximations*of*homomorphic encryption over an*Abelian**group*. ... Theory*of*Homomorphic Encryption over*Two**Abelian**Groups*Definition 17. The theory*of**Abelian**groups*is defined as TAG = (ΣAG, BAG, RAG). ...##
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A simplified scheme for GUT-inspired theories with multiple Abelian factors

2012
*
European Physical Journal C: Particles and Fields
*

Grand Unified Theories often involve additional

doi:10.1140/epjc/s10052-012-1885-5
fatcat:kctxva6l45fddfd6kd65sbswge
*Abelian**group*factors apart from the standard model hypercharge, that generally lead to loop-induced mixing gauge kinetic*terms*. ...*In*this letter, we show that at the one-loop level this effect can be avoided*in*many cases by a suitable choice*of*basis*in**group*space and present a general scheme for the construction*of*this basis. ... Note added: As this paper has been finished there has been a similar work calculating the 1-and 2-loop RGEs for*two*mixing U (1)s*in*a non-diagonal basis, [16] . ...##
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Dimension inference under polymorphic recursion

1995
*
Proceedings of the seventh international conference on Functional programming languages and computer architecture - FPCA '95
*

We show that, under polymorphic recursion, type inference amounts to syntactic

doi:10.1145/224164.224197
dblp:conf/fpca/Rittri95
fatcat:h4ihcnclifdpbhcs2arypklafe
*semi*-*unification**of*proper types, followed by equational*semi*-*unification**of*dimensions. ... We give a polynomial-time algorithm that decides if a*semi*-*unification*problem*in*a vector space can be solved and, if so, returns a most general*semi*-unifier. ... I have failed to construct an algorithm for*semi*-*unification**of*several boxes*in**Abelian**groups*. ...##
###
TeV Physics from the Top Down
[article]

2003
*
arXiv
*
pre-print

Concrete

arXiv:hep-ph/0308033v1
fatcat:l72o73peibarpbuw3lckv4sf5y
*semi*-realistic string/M theory constructions often predict the existence*of*new physics at the TeV scale, which may be different*in*character from the bottom-up ideas that are motivated by specific ... I describe*two*examples, heterotic and open string,*of*such constructions. ... There may be additional non-*abelian**groups**in*the ordinary sector as well. ...##
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Split Supersymmetry in String Theory

2005
*
AIP Conference Proceedings
*

Type I string theory

doi:10.1063/1.2149701
fatcat:gdc47hqxnfai7my7gdjow6wvs4
*in*the presence*of*internal magnetic fields provides a concrete realization*of*split supersymmetry. ... For weak magnetic fields, the correct Standard Model spectrum guarantees gauge coupling*unification*with sin^2θ_W=3/8 at the compactification scale*of*M_ GUT≃ 2 × 10^16 GeV. ...*In*this section, we study precisely the general requirements for satisfying the first*of*the above*two*conditions, namely natural*unification**of*non-*abelian*gauge couplings. ...##
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Advances in old-fashioned heterotic string model building

1998
*
Nuclear Physics B - Proceedings Supplements
*

I review findings

doi:10.1016/s0920-5632(97)00653-1
fatcat:iqegtrbzinaqxhwouo4phx54aa
*of*various research*groups*regarding perturbative heterotic string model building*in*the last 12 months. ... Issues covered include the role*of*U(1)'s and LDS's*in*limiting proton decay, developments*in*classification*of*models containing anomalous U(1), and possible complications resulting from kinetic mixing ...*in*the gauge*group*, and K is the level*of*the gauge*group*. ...##
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Large N_f for multiple representations
[article]

2020
*
arXiv
*
pre-print

The pole structure

arXiv:2005.07540v1
fatcat:jkcnoffr3bh4jhahcwi3boasmm
*in*the beta function is traced back to the intrinsic non-*abelian*nature*of*the gauge*group*, independently on the fermion representation. ... This result validates the conjectured existence*of*an interactive UV fixed point for non-*abelian*gauge theories with large fermion multiplicity. ... Thus, the presence*of*an UV fixed point only comes from the first*term*, i.e. from the non-*abelian*nature*of*each gauge factor*in*the*semi*-simple*group*. ...##
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b–τ Yukawa non-unification in supersymmetric SU(5) with an Abelian flavor symmetry

2004
*
Physics Letters B
*

The model predicts approximate, but never exact, bottom-tau Yukawa

doi:10.1016/j.physletb.2003.10.100
fatcat:bkiztntf6bedflj5wvo6c4o2a4
*unification*. The deviations are related to*group*theoretical coefficients and can naturally be at the level*of*10%-20%. ... We present a supersymmetric SU(5) x U(1)_H model, free from gauge anomalies, where the*Abelian*factor U(1)_H, introduced to account for the hierarchy*of*fermion masses and mixings, is broken by the same ... This work was supported*in*part by Colciencias*in*Colombia. ...
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