canonical involution
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2017 ◽  
Vol 41 ◽  
pp. 854-868
Author(s):  
Hülya KADIOĞLU

2015 ◽  
Vol 14 (08) ◽  
pp. 1550129 ◽  
Author(s):  
Neha Makhijani ◽  
R. K. Sharma ◽  
J. B. Srivastava

Let 𝔽qD2N be the group algebra of D2N, the dihedral group of order 2N, over 𝔽q = GF (q). In this paper, we compute the order of the unitary subgroup of the group of units of 𝔽2kD2N with respect to the canonical involution ∗.


2013 ◽  
Vol 13 (02) ◽  
pp. 1350090 ◽  
Author(s):  
KULDEEP KAUR ◽  
MANJU KHAN

Let p be an odd prime, D2p be the dihedral group of order 2p, and F2 be the finite field with two elements. If * denotes the canonical involution of the group algebra F2D2p, then bicyclic units are unitary units. In this note, we investigate the structure of the group [Formula: see text], generated by the bicyclic units of the group algebra F2D2p. Further, we obtain the structure of the unit group [Formula: see text] and the unitary subgroup [Formula: see text], and we prove that both [Formula: see text] and [Formula: see text] are normal subgroups of [Formula: see text].


2009 ◽  
Vol 52 (2) ◽  
pp. 245-256
Author(s):  
Edgar G. Goodaire ◽  
César Polcino Milies

AbstractLet L be an RA loop, that is, a loop whose loop ring over any coefficient ring R is an alternative, but not associative, ring. Let ℓ ⟼ ℓθ denote an involution on L and extend it linearly to the loop ring RL. An element α ∈ RL is symmetric if αθ = α and skew-symmetric if αθ = –α. In this paper, we show that there exists an involution making the symmetric elements of RL commute if and only if the characteristic of R is 2 or θ is the canonical involution on L, and an involution making the skew-symmetric elements of RL commute if and only if the characteristic of R is 2 or 4.


2006 ◽  
Vol 05 (02) ◽  
pp. 145-151
Author(s):  
ANA C. VIEIRA ◽  
VIVIANE RIBEIRO T. DA SILVA

Let * denote the canonical involution of the group algebra KG induced by the map x ↦ x-1 for x ∈ G. In case K is a real extension of ℚ, we consider Cayley unitary elements built out of skew elements k = α(x - x-1) in KG such that 1 + k is invertible in KG, for α ∈ K and x ∈ G. The constructions involve an interesting sequence in the coefficients of (1 + k)-1 which is the Fibonacci sequence when α = 1.


2005 ◽  
Vol 04 (02) ◽  
pp. 187-194
Author(s):  
MICHITAKU FUMA ◽  
YASUSHI NINOMIYA

Let G be a finite group and H a subgroup of G. The Hecke algebra ℋ(G,H) associated with G and H is defined by the endomorphism algebra End ℂ[G]((ℂH)G), where ℂH is the trivial ℂ[H]-module and (ℂH)G = ℂH⊗ℂ[H] ℂ[G]. As is well known, ℋ(G,H) is a semisimple ℂ-algebra and it is commutative if and only if (ℂH)G is multiplicity-free. In [6], by a ring theoretic method, it is shown that if the canonical involution of ℋ(G,H) is the identity then ℋ(G,H) is commutative and, if there exists an abelian subgroup A of G such that G = AH then ℋ(G,H) is commutative. In this paper, by a character theoretic method, we consider the commutativity of ℋ(G,H).


2002 ◽  
Vol 167 (1) ◽  
pp. 53-82 ◽  
Author(s):  
Thomas Hüttemann ◽  
John R. Klein ◽  
Wolrad Vogell ◽  
Friedhelm Waldhausen ◽  
Bruce Williams

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