ajb Posted March 23, 2009 Share Posted March 23, 2009 Let us work in the [math]\mathbb{Z}_{2}[/math] graded category. A Loday algebra is a "crippled" or "wonky" Lie algebra. That is it satisfies the bracket satisfies the Jacobi identity, but is not skew symmetric. An interesting question is if there exists a homotopy version. I suspect that one can consider "crippled" [math]L_{\infty}[/math] -algebras. So, a series of brackets that satisfy higher Jacobi identities, but do not have a symmetry property. Any body seen anything like that? A differential over such an algebra would also be straight forward to define. I myself have defined notions of a differential [math]L_{\infty}[/math]-algebra and a differential BV-algebra. (We can talk more about these later if anyone is interested). Cheers Link to comment Share on other sites More sharing options...
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