An unpublished theorem of Manfred Schocker and the Patras-Reutenauer algebra
نویسنده
چکیده
Patras, Reutenauer (J. Algebr. Comb. 16:301–314, 2002) describe a subalgebra A of the Malvenuto-Reutenauer algebra P . Their paper contains several characteristic properties of this subalgebra. In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra. In this paper we establish a slightly generalized version of Schocker’s theorem, and give some applications. Finally we describe a derivation of the convolution algebra A, which is a homomorphism for the inner product.
منابع مشابه
Lie Elements and Knuth Relations
A coplactic class in the symmetric group Sn consists of all permutations in Sn with a given Schensted Q-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of Sn which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Re...
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