Classification of maximal rank curves in the liaison class L n

1987 ◽  
Vol 277 (4) ◽  
pp. 585-603 ◽  
Author(s):  
Giorgio Bolondi ◽  
Juan Migliore
Keyword(s):  
Maximal Rank ◽  
Liaison Class

KAC-Moody Lie Algebras and the Classification of Nilpotent Lie Algebras of Maximal Rank

1982 ◽  
Vol 34 (6) ◽  
pp. 1215-1239 ◽  
Author(s):  
L. J. Santharoubane
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Finite Dimension ◽  
Maximal Rank ◽  
Killing Form ◽  
Nilpotent Lie Algebra ◽  
Nilpotent Lie Algebras ◽  
Infinite Dimensional ◽  
Dimensional Version

Introduction. The natural problem of determining all the Lie algebras of finite dimension was broken in two parts by Levi's theorem:1) the classification of semi-simple Lie algebras (achieved by Killing and Cartan around 1890)2) the classification of solvable Lie algebras (reduced to the classification of nilpotent Lie algebras by Malcev in 1945 (see [10])).The Killing form is identically equal to zero for a nilpotent Lie algebra but it is non-degenerate for a semi-simple Lie algebra. Therefore there was a huge gap between those two extreme cases. But this gap is only illusory because, as we will prove in this work, a large class of nilpotent Lie algebras is closely related to the Kac-Moody Lie algebras. These last algebras could be viewed as infinite dimensional version of the semisimple Lie algebras.

Classification and Isomorphisms of Non-degenerate Solvable Lie Algebras of Maximal Rank

2008 ◽  
Vol 15 (02) ◽  
pp. 347-360 ◽  
Author(s):  
Haishan Zhang ◽  
Caihui Lu
Keyword(s):  
Lie Algebras ◽  
Maximal Rank ◽  
Nilpotent Lie Algebras ◽  
Solvable Lie Algebras

The classification of nilpotent Lie algebras of maximal rank was solved by Santharoubane. In the present paper, we prove that the classification of non-degenerate solvable Lie algebras of maximal rank can be obtained from the work of Santharoubane.

scholarly journals Classification of four qubit states and their stabilisers under SLOCC operations

2022 ◽  
Author(s):  
Heiko Dietrich ◽  
Willem A De Graaf ◽  
Alessio Marrani ◽  
Marcos Origlia
Keyword(s):  
Hilbert Space ◽  
Symmetric Space ◽  
Semidirect Product ◽  
Maximal Rank ◽  
Special Case ◽  
Qubit States

Abstract We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2,C)^4 on the Hilbert space H_4 = (C^2)^{\otimes 4}. We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2,C)^4-orbits on H_4. It follows that an element of H_4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parametrised family of elements, and the elements in the same class all have equal stabiliser in SL(2,C)^4. We also present a complete and irredundant classification of elements and stabilisers up to the action of the semidirect product Sym_4\ltimes\SL(2,C)^4 where Sym_4 permutes the four tensor factors of H_4.

Complete classification of finite-dimensional estimation algebras of maximal rank

2003 ◽  
Vol 76 (7) ◽  
pp. 657-677 ◽  
Author(s):  
Stephen S.-T. Yau
Keyword(s):  
Maximal Rank ◽  
Complete Classification ◽  
Finite Dimensional

Novel Classification of Finite Dimensional Filters with Non-maximal Rank Estimation Algebra

2020 ◽  
Author(s):  
Wenhui Dong ◽  
Xiuqiong Chen ◽  
Stephen S.-T. Yau
Keyword(s):  
Maximal Rank ◽  
Rank Estimation ◽  
Finite Dimensional ◽  
Estimation Algebra

Classification of metabelian Lie algebras of maximal rank

2001 ◽  
Vol 332 (11) ◽  
pp. 969-974
Author(s):  
Desamparados Fernández-Ternero ◽  
Juan Núñez-Valdés
Keyword(s):  
Lie Algebras ◽  
Maximal Rank
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