Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

نویسندگان

چکیده

This paper presents a classification of 7-dimensional real and complex indecomposable solvable Lie algebras having some 5-dimensional nilradicals. Afterwards, we combine our results with those Rubin Winternitz (1993), Ndogmo (1994), Snobl (2005, 2009), Karasek (2010) to obtain complete In association Gong (1998), Parry (2007), Hindeleh Thompson (2008), achieve algebras.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Solvable Lie algebras with triangular nilradicals

All finite-dimensional indecomposable solvable Lie algebras L(n, f), having the triangular algebra T (n) as their nilradical, are constructed. The number of nonnilpotent elements f in L(n, f) satisfies 1 ≤ f ≤ n− 1 and the dimension of the Lie algebra is dim L(n, f) = f + 1 2 n(n − 1).

متن کامل

On a Subclass of 5-dimensional Solvable Lie Algebras Which Have 3-dimensional Commutative Derived Ideal

The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e., five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbit) are orbit of zero or maximal dimension. The main results of the paper is the classification up to an isomorphism of all MD5-algebras G with the derived ideal G1 := [G,G] is a 3-dimensional commuta...

متن کامل

Classification of Solvable Lie Algebras

Several classifications of solvable Lie algebras of small dimension are known. Up to dimension 6 over a real field they were classified by G. M. Mubarakzjanov [Mubarakzjanov 63a, Mubarakzjanov 63b], and up to dimension 4 over any perfect field by J. Patera and H. Zassenhaus [Patera and Zassenhaus 90]. In this paper we explore the possibility of using the computer to obtain a classification of s...

متن کامل

Degenerations of 7-dimensional Nilpotent Lie Algebras

We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimen...

متن کامل

Classification of Finite-dimensional Semisimple Lie Algebras

Every finite-dimensional Lie algebra is a semi-direct product of a solvable Lie algebra and a semisimple Lie algebra. Classifying the solvable Lie algebras is difficult, but the semisimple Lie algebras have a relatively easy classification. We discuss in some detail how the representation theory of the particular Lie algebra sl2 tightly controls the structure of general semisimple Lie algebras,...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Communications in Algebra

سال: 2022

ISSN: ['1532-4125', '0092-7872']

DOI: https://doi.org/10.1080/00927872.2022.2145300