Dimension quotients of metabelian Lie rings

nilpotent quotients in finitely presented Lie rings †

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...

Computing nilpotent quotients in finitely presented Lie rings

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...

On the Classification of Metabelian Lie Algebras(')

The classification of 2-step nilpotent Lie algebras is attacked by a generator-relation method. The main results are in low dimensions or a small number of relations. Introduction. According to a theorem of Levi, in characteristic zero a finitedimensional Lie algebra can be written as the direct sum of a semisimple subalgebra and its unique maximal solvable ideal. If the field is algebraically ...

Quotients of Representation Rings

We give a proof using so-called fusion rings and q-deformations of Brauer algebras that the representation ring of an orthogonal or symplectic group can be obtained as a quotient of a ring Gr(O(∞)). This is obtained here as a limiting case for analogous quotient maps for fusion categories, with the level going to ∞. This in turn allows a detailed description of the quotient map in terms of a re...

Rings of Quotients of Rings of Functions