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

Franz Baader, Werner Nutt
1991 Lecture Notes in Computer Science  
The class encompasses important examples like the theories 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  ... 
doi:10.1007/3-540-53904-2_91 fatcat:6jzlkhtkxnccfmbmwzr3xccnra

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- groupin 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.  ... 

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

Scott Chapman
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 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.  ... 
arXiv:1911.04593v4 fatcat:onqkz4xsqfgszaosf6klukahxu

Homogeneous Equations of Algebraic Petri Nets [article]

Marvin Triebel, Jan Sürmeli
2016 arXiv   pre-print
One way to specify correctness 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  ... 
arXiv:1606.05490v3 fatcat:doq5fctxejdxhf4keed34nmngy

Homogeneous Equations of Algebraic Petri Nets

Marvin Triebel, Jan Sürmeli, Marc Herbstritt
2016 International Conference on Concurrency Theory  
One way to specify correctness 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  ... 
doi:10.4230/lipics.concur.2016.14 dblp:conf/concur/TriebelS16 fatcat:hvsqmznhtngpxalnce5wvjz4zi

Unification mechanism for gauge and spacetime symmetries

András László
2017 Journal of Physics A: Mathematical and Theoretical  
A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced.  ...  theorems in a non-supersymmetric way.  ...  in terms of two-spinors.  ... 
doi:10.1088/1751-8121/aa5c04 fatcat:lldkkynrrnd5xgudvjgtcaw2ui

Theories of Homomorphic Encryption, Unification, and the Finite Variant Property

Fan Yang, Santiago Escobar, Catherine Meadows, José Meseguer, Paliath Narendran
2014 Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming - PPDP '14  
an 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).  ... 
doi:10.1145/2643135.2643154 dblp:conf/ppdp/YangEMMN14 fatcat:ss5awwz6wffnnlp6i67rg5svcu

A simplified scheme for GUT-inspired theories with multiple Abelian factors

Felix Braam, Jürgen Reuter
2012 European Physical Journal C: Particles and Fields  
Grand Unified Theories often involve additional 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] .  ... 
doi:10.1140/epjc/s10052-012-1885-5 fatcat:kctxva6l45fddfd6kd65sbswge

Dimension inference under polymorphic recursion

Mikael Rittri
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 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.  ... 
doi:10.1145/224164.224197 dblp:conf/fpca/Rittri95 fatcat:h4ihcnclifdpbhcs2arypklafe

TeV Physics from the Top Down [article]

Paul Langacker
2003 arXiv   pre-print
Concrete 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.  ... 
arXiv:hep-ph/0308033v1 fatcat:l72o73peibarpbuw3lckv4sf5y

Split Supersymmetry in String Theory

I. Antoniadis
2005 AIP Conference Proceedings  
Type I string theory 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.  ... 
doi:10.1063/1.2149701 fatcat:gdc47hqxnfai7my7gdjow6wvs4

Advances in old-fashioned heterotic string model building

Gerald B. Cleaver
1998 Nuclear Physics B - Proceedings Supplements  
I review findings 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.  ... 
doi:10.1016/s0920-5632(97)00653-1 fatcat:iqegtrbzinaqxhwouo4phx54aa

Large N_f for multiple representations [article]

Giacomo Cacciapaglia, Shahram Vatani
2020 arXiv   pre-print
The pole structure 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.  ... 
arXiv:2005.07540v1 fatcat:jkcnoffr3bh4jhahcwi3boasmm

b–τ Yukawa non-unification in supersymmetric SU(5) with an Abelian flavor symmetry

Diego Aristizabal, Enrico Nardi
2004 Physics Letters B  
The model predicts approximate, but never exact, bottom-tau Yukawa 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.  ... 
doi:10.1016/j.physletb.2003.10.100 fatcat:bkiztntf6bedflj5wvo6c4o2a4
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