Embedding algebras into the Leavitt algebra of module type (1, 2).

Time: 9h30, Wednesday, 04/02/2026

Venue: Room 612, Building A6

Abstract: Since the commutative monoid $T = (\{0, 1\}, \vee)$ is a weak terminal object in the category of conical monoids with order units, there is a unital homomorphism from every Bergman $K$-algebra corresponding to a conical finitely generated commutative monoid into the Leavitt algebra $L_K(1,2)$, where $K$ is a field. This fact will be used to give a short proof that Leavitt path algebras associated with finite graphs with condition $(L)$  embed into $L_K(1,2)$, as well as provide criteria for an embedding of $M_s(L_{K}(1, m))$ in $M_s(L_{K}(1, n))$. As our second main result, we show that the Heisenberg equation $xy-yx=1$ cannot be realized in any Steinberg algebra, implying that the first Weyl algebra cannot be embedded into $L_K(1,2)$, giving an affirmative answer to a question of  Brownlowe and S\o rensen on the embeddability of $K$-algebras  with a countable basis inside $L_K(1,2)$.  This is joint work with Boris Bilich and Roozbeh Hazrat.