**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32731

##### Computational Algorithm for Obtaining Abelian Subalgebras in Lie Algebras

**Authors:**
Manuel Ceballos,
Juan Nunez,
Angel F. Tenorio

**Abstract:**

**Keywords:**
Solvable Lie algebra,
maximal abelian dimension,
algorithm.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1077249

**References:**

[1] J.C. Benjumea, F.J. Echarte, J. N'u╦£nez and A.F. Tenorio, "An Obstruction to Represent Abelian Lie Algebras by Unipotent Matrices," Extracta Math., vol. 19, pp. 269-277, 2004.

[2] J.C. Benjumea, J. N'u╦£nez and A.F. Tenorio, "The Maximal Abelian Dimension of Linear Algebras formed by Strictly Upper Triangular Matrices," Theor. Math. Phys., vol. 152, pp. 1225-1233, 2007.

[3] M. Ceballos, J. N'u╦£nez and A.F. Tenorio, "The Computation of Abelian Subalgebras in the Lie Algebra of Upper-Triangular Matrices," An. St. Univ. Ovidius Constanta, vol. 16, pp. 59-66, 2008.

[4] M. Krawtchouk, "U┬¿ ber vertauschbare Matrizen," Rend. Circolo Mat. Palermo Serie I, vol. 51, pp. 126-130, 1927.

[5] T.J. Laffey, "The minimal dimension of maximal commutative subalgebras of full matrix algebras," Linear Alg. Appl., vol. 71, pp. 199-212,1985.

[6] D.A. Suprunenko and R.I. Tyshkevich, "Commutative Matrices". New York: Academic Press, 1968.

[7] A.F. Tenorio, "Solvable Lie Algebras and Maximal Abelian Dimensions," Acta Math. Univ. Comenian. (N.S.), vol. 77, pp. 141-145, 2008.

[8] J.-L. Thiffeault and P.J. Morrison, "Classification and Casimir Invariants of Lie-Poisson Brackets," Phys. D, vol. 136, pp. 205-244, 2000.

[9] V.S. Varadarajan, "Lie Groups, Lie Algebras and Their Representations". New York: Springer, 1984.