The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Takeo Matsuoka - One of the best experts on this subject based on the ideXlab platform.
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Semidirect Product gauge group su 3 _ rm c times su 2 _ rm l rtimes u 1 _ rm y and quantization of hypercharge
Physical Review D, 2011Co-Authors: Chuichiro Hattori, Mamoru Matsunaga, Takeo MatsuokaAbstract:In the standard model the hypercharges of quarks and leptons are not determined by the gauge group SU(3){sub c}xSU(2){sub L}xU(1){sub Y} alone. We show that, if we choose the Semidirect Product group [SU(3){sub c}xSU(2){sub L}]xU(1){sub Y} as its gauge group, the hyperchages are settled to be n/6 mod Z(n=0,1,3,4). In addition, the conditions for gauge-anomaly cancellation give strong constraints. As a result, the ratios of the hypercharges are uniquely determined and the gravitational anomaly is automatically canceled. The standard charge assignment to quarks and leptons can be properly reproduced. For exotic matter fields their hypercharges are also discussed.
Charles H. Conley - One of the best experts on this subject based on the ideXlab platform.
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Representations of finite length of Semidirect Product Lie groups
Journal of Functional Analysis, 1993Co-Authors: Charles H. ConleyAbstract:Abstract We treat a part of the program of studying the correspondence between orbits and representations of finite length. In Section 1 we prove that it is possible to divide a regular distribution by a function so that the quotient is a regular distribution, under suitable conditions on the function. In Section 2 the results of Section 1 are used to prove that all representations of finite flag length of a vector group, realized in a vector bundle over a submanifold of the dual, act by endomorphisms of the bundle. In Section 3 the results of Section 2 are used to give an extension of the Mackey functor to representations of Semidirect Product Lie groups with a fixed composition series.
Vladimir Shpilrain - One of the best experts on this subject based on the ideXlab platform.
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using Semidirect Product of semi groups in public key cryptography
arXiv: Cryptography and Security, 2016Co-Authors: Delaram Kahrobaei, Vladimir ShpilrainAbstract:In this survey, we describe a general key exchange protocol based on Semidirect Product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This protocol can be based on any group or semigroup, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when this protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. The focus then shifts to selecting an optimal platform (semi)group, in terms of security and efficiency. We show, in particular, that one can get a variety of new security assumptions by varying an automorphism used for a (semi)group extension.
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Public key exchange using Semidirect Product of (semi)groups
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2013Co-Authors: Maggie Habeeb, Charalambos Koupparis, Delaram Kahrobaei, Vladimir ShpilrainAbstract:In this paper, we describe a brand new key exchange protocol based on a Semidirect Product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. Here we also suggest a particular non-commutative semigroup (of matrices) as the platform and show that security of the relevant protocol is based on a quite different assumption compared to that of the standard Diffie-Hellman protocol.
W Van Dam - One of the best experts on this subject based on the ideXlab platform.
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from optimal measurement to efficient quantum algorithms for the hidden subgroup problem over Semidirect Product groups
Foundations of Computer Science, 2005Co-Authors: Dave Bacon, Andrew M Childs, W Van DamAbstract:We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the Semidirect Product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem. By solving this problem, we find efficient quantum algorithms for a number of nonabelian hidden subgroup problems, including some for which no efficient algorithm was previously known: certain metacyclic groups as well as all groups of the form /spl Zopf//sub p/ /sup r/ /spl times/ /spl Zopf//sub p/ fixed r (including the Heisenberg group, r = 2). In particular our results show that entangled measurements across multiple copies of hidden subgroup states can be useful for efficiently solving the nonabelian HSP.
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from optimal measurement to efficient quantum algorithms for the hidden subgroup problem over Semidirect Product groups
arXiv: Quantum Physics, 2005Co-Authors: Dave Bacon, Andrew M Childs, W Van DamAbstract:We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the Semidirect Product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem. By solving this problem, we find efficient quantum algorithms for a number of nonabelian hidden subgroup problems, including some for which no efficient algorithm was previously known: certain metacyclic groups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including the Heisenberg group, r=2). In particular, our results show that entangled measurements across multiple copies of hidden subgroup states can be useful for efficiently solving the nonabelian HSP.
H. Montani - One of the best experts on this subject based on the ideXlab platform.
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double lie algebras Semidirect Product and integrable systems
arXiv: Mathematical Physics, 2014Co-Authors: Santiago Capriotti, H. MontaniAbstract:We study integrable systems on double Lie algebras in absence of Adinvariant bilinear form by passing to the Semidirect Product with the �representation. We show that in this stage a natural Ad-invariant bilinear form does exist, allowing for a straightforward application of the AKS theory, and giving rise to Manin triple structure, thus bringing the problem to the realm of Lie bialgebras and Poisson-Lie groups.
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Integrable systems on Semidirect Product Lie groups
Journal of Physics A: Mathematical and Theoretical, 2014Co-Authors: Santiago Capriotti, H. MontaniAbstract:We study integrable systems on the Semidirect Product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this Semidirect Product Lie group structure, we construct a class of symplectic submanifolds equipped with a Dirac bracket on which integrable systems (in the Adler–Kostant–Symes sense) are naturally built through collective dynamics. In doing so, we address other issues such as factorization, Poisson–Lie structures and dressing actions. We show that the procedure becomes recursive for some particular Hamilton functions, giving rise to a tower of nested integrable systems.
