In 2009, Gyurko introduced $\Pi$-rough path which extends $p$-rough path. Inspired by this work we introduce the degree-$(\Pi,N)$ signature which can be treated as the step-$N$ signature for some $\Pi$. The degree-$(\Pi,N)$ signature holds some algebraic properties which will be proven in this paper.
Rough path, signature, Lie group, Lie algebra
"The extension of step-$N$ signatures,"
Turkish Journal of Mathematics: Vol. 45:
3, Article 17.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss3/17