Aust. J. Math. Anal. Appl. Vol. 17 (2020), No. 2, Art. 9, 9 pp. AJMAA SOME PROPERTIES OF (CO)HOMOLOGY OF LIE ALGEBRA ALAA HASSAN NORELDEEN MOHAMED, HEGAGI MOHAMED ALI, SAMAR ABOQUOTA Received 2 December, 2019; accepted 14 July, 2020; published 30 September, 2020. DEPARTMENT OF MATHEMATICS,FACULTY OF SCIENCE,ASWAN UNIVERSITY,ASWAN,EGYPT. ala2222000@yahoo.com hegagi_math@aswu.edu.eg scientist_samar@yahoo.com ABSTRACT. Lie algebra is one of the important types of algebras. Here, we studied lie algebra and discussed its properties. Moreover, we define the Dihedral homology of lie algebra and prove some relations among Hochschild, Cyclic and Dihedral homology of lie algebra. Finally, we prove the Mayer-vetories sequence on Dihedral homology of lie algebra and proved that HC n (g,M ) ∼ = - HD n (g,M )  + HD n (g,M ). Key words and phrases: Lie algebra; Cyclic homology; Dihedral homology. 2010 Mathematics Subject Classification. 17B55, 17B56. ISSN (electronic): 1449-5910 c  2020 Austral Internet Publishing. All rights reserved. The producer passes on unique gratefulness to the experts for their recognize suggestion and help in the major draft of the present working.