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We study the structure of an arbitrary graded Lie triple system ${\mathfrak T}$ with restrictions neither on the dimension nor the base field. We show that ${\mathfrak T}$ is of the form ${\mathfrak T}=U + \sum_{j}I_{j}$ with $U$ a linear subspace of the 1-homogeneous component ${\mathfrak T}_1$ and any $I_{j}$ a well described graded ideal of ${\mathfrak T}$, satisfying $[I_j,{\mathfrak T},I_k]=0$ if $j\neq k$. Under mild conditions, the simplicity of ${\mathfrak T}$ is characterized and it is shown that an arbitrary graded Lie triple system ${\mathfrak T}$ is the direct sum of the family of its minimal graded ideals, each one being a simple graded Lie triple system.
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참고문헌 (34)
참고문헌 신청
Y. A. Bahturin / 2006 / Group gradings on simple Lie algebras of type A / J. Lie Theory 16(4):719~742
V. K. Balachandran / 1972 / Real L∗-algebras / Indian J. Pure Appl. Math 3(6):1224~1246
G. Benkart / 2004 / A(n, n)-graded Lie superalgebras / J. Reine Angew. Math 573:139~156
M. Boussahel / 2011 / Graded Lie algebra and the U(3)L ×U(1)N gauge model / Internat. J. Modern Phys. A 26(5):873~909
C. Boyallian / 2008 / Quasifinite representations of the Lie superalgebra of quantum pseudodifferential operators / J. Math. Phys 49(2):13
V. K. Balachandran / 1972 / Real L∗-algebras / Indian J. Pure Appl. Math 3(6):1224~1246
G. Benkart / 2004 / A(n, n)-graded Lie superalgebras / J. Reine Angew. Math 573:139~156
M. Boussahel / 2011 / Graded Lie algebra and the U(3)L ×U(1)N gauge model / Internat. J. Modern Phys. A 26(5):873~909
C. Boyallian / 2008 / Quasifinite representations of the Lie superalgebra of quantum pseudodifferential operators / J. Math. Phys 49(2):13
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