140 citations · 1.3k across the 89 of their papers we have counts for
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On extensive amenability of algebras
Laurent Bartholdi
For a module \(M\) over a cocommutative Hopf algebra \(\mathscr A\), we define extensive amenability by amenability of its symmetric algebra as a module over \(\operatorname{Sym}(M…
Amenability of Lie, Group and Hopf algebras
Laurent Bartholdi
We propose to define amenability of a Lie algebra by the existence of almost-invariant finite-dimensional subcoalgebras of its universal enveloping algebra. More generally, a modul…
On Gardam's and Murray's units in group rings
Laurent Bartholdi
We show that the units found in torsion-free group rings by Gardam are twisted unitary elements. This justifies some choices in Gardam's construction that might have appeared arbit…
Wreath products of cocommutative Hopf algebras
Laurent Bartholdi, Olivier Siegenthaler, Todd Trimble
We define wreath products of cocommutative Hopf algebras, and show that they enjoy a universal property for coalgebra-split extensions, analogous to the Kaloujnine-Krasner theorem…
Lie Dimension Subrings
Laurent Bartholdi, Inder Bir S. Passi
We compare, for L a Lie ring over the integers, its lower central series (γ_n(L))_{n>0} and its dimension series defined by δ_n(L):=L\cap \varpi^n(L) in the universal enveloping al…
Images of Golod-Shafarevich algebras with small growth
Agata Smoktunowicz, Laurent Bartholdi
We show that Golod-Shafarevich algebras can be homomorphically mapped onto infinite-dimensional algebras with polynomial growth, under mild assumptions of the number of relations o…
On a conjecture of Goodearl: Jacobson radical non-nil algebras of Gelfand-Kirillov dimension 2
Agata Smoktunowicz, Laurent Bartholdi
For an arbitrary countable field, we construct an associative algebra that is graded, generated by finitely many degree-1 elements, is Jacobson radical, is not nil, is prime, is no…
Self-similar Lie algebras
Laurent Bartholdi
We give a general definition of self-similar Lie algebras, and show that important examples of Lie algebras fall into that class. We give sufficient conditions for a self-similar L…
Groups and Lie algebras corresponding to the Yang-Baxter equations
Laurent Bartholdi, Benjamin Enriquez, Pavel Etingof +1
For a positive integer n we introduce quadratic Lie algebras tr_n qtr_n and discrete groups Tr_n, QTr_n naturally associated with the classical and quantum Yang-Baxter equation, re…
Branch Rings, Thinned Rings, Tree Enveloping Rings
Laurent Bartholdi
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring…