Antipodes and involutions
نویسندگان
چکیده
If H is a connected, graded Hopf algebra, then Takeuchi’s formula can be used to compute its antipode. However, there is usually massive cancellation in the result. We show how sign-reversing involutions can sometimes be used to obtain cancellationfree formulas. We apply this idea to the Hopf algebras of polynomials, graphs, and noncommutative symmetric functions.
منابع مشابه
As many antipodes as vertices on convex polyhedra
An earlier result states that, on the surface of a convex polyhedron with vertices endowed with its intrinsic metric, a point cannot have more than antipodes (farthest points). In this paper we produce examples of polyhedra with vertices, on which some suitable point admits exactly antipodes. We also proved that, for any positive number 1, there exist (in the closure of the set of these polyhed...
متن کاملAs many antipodes as vertices on some convex polyhedra
An earlier result states that a point of the surface of a convex polyhedron with n vertices, endowed with its intrinsic metric, cannot have more than n antipodes (farthest points). In this paper we produce examples of polyhedra with n vertices, on which some suitable point admits exactly n antipodes. MSC (2000): 52B10, 53C45.
متن کاملInvolution Matrices of Real Quaternions
An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.
متن کاملInvolutions of a Clifford algebra induced by involutions of orthogonal group in characteristic 2
Among the involutions of a Clifford algebra, those induced by the involutions of the orthogonal group are the most natural ones. In this work, several basic properties of these involutions, such as the relations between their invariants, their occurrences and their decompositions are investi-
متن کاملQuaternion Involutions
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such involutions, and we show that the quaternions have an infinite number of involutions. We show that the conjugate of a quaternion may be expressed using three mu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 148 شماره
صفحات -
تاریخ انتشار 2017