No description available.

No description available.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / Includes bibliographical references. / Ph.D.

We construct a Lie relator which is not an identical Lie relator. This is the first known example of a non-identical Lie relator. Next we consider the existence of torsion in outer commutator groups. Let L be a free Lie ring. Suppose that 1 < i ≤ j ≤ 2i and i ≤ k ≤ i + j + 1. We prove that L/[L^j, Lⁱ, L^k<./em>] is torsion free. Also, we prove that if 1 < i ≤ j ≤ 2i and j ≤ k ≤ l ≤ i + j then L/[L^j, Lⁱ, L^k, L^l] is torsion free. We then prove that the analogous groups, namely F/[γ_j(F),γ_i(F),γ_k(F)] and F/[γ_j(F),γ_i(F),γ_k(F),γ_l(F)] (under the same conditions for i, j, k and i, j, k, l respectively), are residually nilpotent and torsion free. We prove the existence of 2-torsion in the Lie rings L/[L^j, Lⁱ, L^k] when 1 ≤ k < i,j ≤ 5, and thus show that our methods do not work in these cases. Finally, we consider the order of finite groups of exponent 8. For m ≥ 2, we define the function T(m,n) by T(m,1) = m and T(m,k + 1) = m^T(m,k). We prove that if G is a finite m-generator group of exponent 8 then |G| ≤ T(m, 7⁴⁷¹), improving upon the best previously known bound of T(m, 8⁸⁸).

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2009. / Includes bibliographical references (p. 47-48).

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Tese (doutorado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2016. / Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2017-01-31T19:18:53Z No. of bitstreams: 1 2016_IlanaZuilaMonteiroAlves.pdf: 1504757 bytes, checksum: 74f9b76f5b924214935e8089f8d39f28 (MD5) / Approved for entry into archive by Raquel Viana(raquelviana@bce.unb.br) on 2017-02-10T21:41:58Z (GMT) No. of bitstreams: 1 2016_IlanaZuilaMonteiroAlves.pdf: 1504757 bytes, checksum: 74f9b76f5b924214935e8089f8d39f28 (MD5) / Made available in DSpace on 2017-02-10T21:41:58Z (GMT). No. of bitstreams: 1 2016_IlanaZuilaMonteiroAlves.pdf: 1504757 bytes, checksum: 74f9b76f5b924214935e8089f8d39f28 (MD5) / Seja L uma álgebra de Lie sobre um corpo de característica p>0. Estudamos a estrutura de álgebra de Lie da álgebra de Poisson simétrica truncada s(L). Isto é, determinamos as condições necessárias e suficientes para L com respeito as quais s(L) é Lie nilpotente, Lie nilpotente forte, csoolnúdvieçlõ ees seosltúavbeel lefocridtea,s ,o nedspee cpirfeiccaismaomso sa cpl>a2s spea drae eLsietu ndialpr oatê nscoialu bfoilirdtea ddee. sC(oLm). Arelésmpe idtois saos, provamos que a classe de Lie nilpotência coincide com a classe de Lie nilpotência forte no caso p>3. Em nossa abordagem, usamos uma teoria bem estabelecida de delta-conjuntos para álgebras de Lie e teoria de relações idênticas para álgebras de Poisson. Também estudamos filtrações em álgebras de Poisson e provamos resultados sobre os produtos dos termos das séries centrais inferiores para álgebras de Poisson. Shestakov provou que a álgebra simétrica s(L) de uma álgebra de Lie arbitrária L, satisfaz a identidade de Poisson {x,{y,z}}≡ 0 se, e somente se, L é abeliana. Estendemos este resultado para Lie nilpotência e Lie solubilidade de S(L). / Let L be a Lie algebra over a field of characteristic p>0. We study the Lie algebra structure of the truncated symmetric Poisson algebra s(L). Namely, we determine the necessary and sufficient conditions for L under which s(L)is Lie nilpotent, Lie strongly nilpotent, solvable and strongly tshoelv satbrolen,g w Lhiee rnei lpwoet enneceyd c lpa>s2s otof ss(tLu)d. yM tohree osvoelvra, bwielit yp.r oUvned tehra et sthtaeb Lliiseh neidlp ocotenndcityio cnlass, sw ceo isnpceidceifsy with the strong Lie nilpotency class in case p>3. In our approach, we use a well-established theory of delta-sets for Lie algebras and theory of identical relations of Poisson algebras. Also, we study filtrations in Poisson algebras and prove results on products of the terms of the lower central series for Poisson algebras. Shestakov proved that the symmetric algebra S(L) of an arbitrary Lie algebra L satisfies the Poisson identity {x,{y,z}}≡0 if, and only if, L is abelian. We extend this result for Lie nilpotency and Lie solvability of S(L).

En esta nota se exponen los principios básicos de la cuantización de álgebras de Poisson, con especial atención al caso del álgebra simétrica de un álgebra de Lie.

No description available.

Lie Groups occur in math and physics as representations of continuous symmetries and are often described in terms of their Lie Algebra. This thesis is concerned with finding a concrete description of a Lie group given its associated Lie algebra. Several calculations toward this end are developed and then implemented in the Maple Differential Geometry package. Examples of the calculations are given.