8 problems

A Lie algebra is an algebra with a bilinear alternating bracket satisfying the Jacobi identity, and a lieon is a basic Lie-algebraic building block from which Lie algebras can be a…

Decomposition conjecture. For $n>2$, any $n$-Filippov algebra splits into the direct product of a trivial $n$-Filippov algebra and a number of non-trivial $n$-Filippov algebras of…

Induced involution conjecture. The map $\iota$ induces an $R$-algebra involution on $\mathcal{Z}_{v,R}$.

Involution compatibility conjecture. For every $\mathfrak{s}\in\mathcal{I}$,

The paper considers two algorithms for deciding quantifier-free definability in finite algebraic structures: the Merging Algorithm, which partitions all tuples of a specified arity…

Frégier's conjecture. Similar theories should exist for most algebraic structures, with a unified treatment based on differential graded Lie algebras.

Algebraic-expression causal-set conjecture. Any associative algebraic expression gives a causal set.

Generalized center decomposition conjecture. The generalized center satisfies