4 papers
The Parafree Conjecture for associative algebras
Vasily Ionin, Roman Mikhailov
For every base field, we construct a finitely generated parafree augmented associative algebra with countably infinite-dimensional second homology. This disproves the analogue of t…
Ping-pong for basis-conjugating HNN-extension of free group
Vasily Ionin
We isolate a tractable class of HNN-extensions of a free group, namely, multiple HNN-extensions by basis-conjugating embeddings. For this class, we construct a normal form and esta…
Functorial languages in homological algebra and lower central series
Nikita Golub, Vasily Ionin, Lev Mukoseev
There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories…
On injectivity of Cohen-Wu homomorphism
Vasily Ionin
We give a new elementary proof of the theorem that a natural map from Milnor's construction to the simplicial group of pure braids is injective. Our approach…