## 26 Citations

### Lower Central Series Quotients of Finitely Generated Algebras over the Integers

- Mathematics
- 2013

We study the lower central series that has elementsL1 = A,L2 = [L1, A] . . . , Lk = [Lk−1, A], . . . for unital associative graded algebras A over Z. Specifically, we consider the quotients Bk =…

### An algebro-geometric construction of lower central series of associative algebras

- Mathematics
- 2015

The lower central series invariants M_k of an associative algebra A are the two-sided ideals generated by k-fold iterated commutators; the M_k provide a filtration of A. We study the relationship…

### LOWER CENTRAL SERIES OF A FREE ASSOCIATIVE ALGEBRA OVER THE INTEGERS AND FINITE FIELDS

- Mathematics
- 2012

### ON THE LOWER CENTRAL SERIES OF PI-ALGEBRAS

- Mathematics
- 2014

In this paper we study the lower central series {Li}i≥1 of algebras with polynomial identities. More specifically, we investigate the properties of the quotients Ni = Mi/Mi+1 of successive ideals…

### Relations in universal Lie nilpotent associative algebras of class 4

- Mathematics
- 2013

ABSTRACT Let K be a unital associative and commutative ring and let K⟨X⟩ be the free unital associative K-algebra on a non-empty set X of free generators. Define a left-normed commutator inductively…

### Identidades de Lie da álgebra de Poisson simétrica truncada

- Mathematics
- 2016

Let L be a Lie algebra over a field of characteristic p > 0. We study the Lie algebra structure of the truncated symmetric Poisson algebra s(L). Namely, we determine the necessary and sufficient…

### On the $\mathrm{GL}(n)$-module structure of Lie nilpotent associative relatively free algebras

- Mathematics
- 2022

Let K 〈X〉 denote the free associative algebra generated by a set X = {x1, . . . , xn} over a field K of characteristic 0. Let Ip, for p ≥ 2, denote the two-sided ideal in K 〈X〉 generated by all…

## References

SHOWING 1-10 OF 14 REFERENCES

### An upper bound for the lower central series quotients of a free associative algebra

- Mathematics
- 2008

Feigin and Shoikhet conjectured in math/0610410 that successive quotients $B_m(A_n)$ of the lower central series filtration of a free associative algebra $A_n$ have polynomial growth. In this paper…

### Quantization of coboundary Lie bialgebras

- Mathematics
- 2006

We show that any coboundary Lie bialgebra can be quantized. For this, we prove that: (a) Etingof-Kazhdan quantization functors are compatible with Lie bialgebra twists, and (b) if such a quantization…

### On $[A,A]/[A,[A,A]]$ and on a $W_n$-action on the consecutive commutators of free associative algebras

- Mathematics
- 2006

We consider the lower central series of the free associative algebra $A_n$ with $n$ generators as a Lie algebra. We consider the associated graded Lie algebra. It is shown that this Lie algebra has a…

### IRREDUCIBLE REPRESENTATIONS OF INFINITE-DIMENSIONAL LIE ALGEBRAS OF CARTAN TYPE

- Mathematics
- 1974

In this paper the irreducible representations of infinite-dimensional filtered Lie algebras are studied. The concept of the height of a representation is introduced, and it is proved that the…

### The Magma Algebra System I: The User Language

- Computer ScienceJ. Symb. Comput.
- 1997

The MAGMA language is presented, the design principles and theoretical background are outlined, and the constructors for structures, maps, and sets are outlined.

### Cohomologies of Lie Groups and Lie Algebras

- Lie Groups and Lie Algebras II
- 2000

### Categories tensorielles

- Mosc Math. J
- 2002