lattice representation
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2020 ◽  
Vol 108 (3) ◽  
pp. 332-340
Author(s):  
ROGER BUNN ◽  
DAVID GROW ◽  
MATT INSALL ◽  
PHILIP THIEM

Let $p$ be an odd prime. The unary algebra consisting of the dihedral group of order $2p$, acting on itself by left translation, is a minimal congruence lattice representation of $\mathbb{M}_{p+1}$.





Biosystems ◽  
2018 ◽  
Vol 173 ◽  
pp. 273-280
Author(s):  
Yukio-Pegio Gunji ◽  
Igor Balaz


Author(s):  
Hyeongseok Kim ◽  
Woon Hyun Lee ◽  
Myeonggil Yeom ◽  
Jeongchang Kim ◽  
Sung Ik Park ◽  
...  


Author(s):  
PHILIP FEINSILVER

Starting with the zero-square "zeon algebra," the regular representation gives rise to a Boolean lattice representation of sl(2). We detail the su(2) content of the Boolean lattice, providing the irreducible representations carried by the algebra generated by the subsets of an n-set. The group elements are found, exhibiting the "special functions" in this context. The corresponding Leibniz rule and group law are shown. Krawtchouk polynomials, the Hamming and the Johnson schemes appear naturally. Applications to the Boolean poset and the structure of Hadamard–Sylvester matrices are shown as well.



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