NOVELTY - A metathesis catalyst compound comprising indenylene ligand, is new.    USE - For producing alpha-olefin, form feed material (such as feed oil); or triacylglyceride, unsaturated fatty acid, or unsaturated fatty acid ester and/or unsaturated fatty acid alkyl ester, which are preferably derived from biodiesel; or triacylglyceride, fatty acid, fatty acid alkyl ester, and/or fatty acid ester derived from seed oil; and alkene; where the alpha olefin is linear 4-24C alpha-olefin (preferably ethylene, propylene, butene, hexane, or octane; especially 1-butene, 1-decene, or 1-heptene) (claimed). The alpha-olefins are useful for forming poly-alpha-olefins (PAOs).    ADVANTAGE - The metathesis catalysts demonstrate high activity and selectivity in metathesis cross-reactions, including ethenolysis, and can be synthesized by mild and affordable synthetic routes. The catalyst compounds are both mild and commercially economical, and provide atom-economical route to desirable olefins, in particular alpha-olefins. The metathesis catalyst compounds demonstrate improved activity and selectivity towards ethenolysis products in ethylene cross-metathesis reactions. The process for production of alpha-olefin (preferably linear 4-24C alpha-olefin) by using the metathesis catalyst compound (I) has a productivity of at least 200 g of linear alpha-olefin per mmol of catalyst per hour; a selectivity of at least 20 wt.% linear alpha-olefin, based upon the weight to the material exiting the reactor; a turnover number, defined as the moles of alpha olefin formed per mol of catalyst, of at least 10000; a yield, when converting unsaturated fatty acids, unsaturated fatty acid esters, and/or unsaturated fatty acid alkyl esters, of ( greater than or equal to 30, preferably greater than or equal to 60)%, where the yield is defined as the moles of alpha olefin formed per mol of unsaturated fatty acids, unsaturated fatty acid esters, and/or unsaturated fatty acid alkyl esters introduced into the reactor; and a yield, when converting triacylglycerides (TAGs) (comprising a compound of formula CH2(-O-C(=O)-R'a)-CH(-O-C(=O)-R'b)-CH2(-O-C(=O)-R'c, where R'a, R'b and R'c are saturated or unsaturated hydrocarbon chain), of greater than or equal to 30%, where the yield is defined as the moles of alpha olefin formed divided by (the moles of unsaturated R'a + moles of unsaturated R'b + moles of unsaturated R'c) introduced into the reactor.    DETAILED DESCRIPTION - A metathesis catalyst compound comprising indenylene ligand, of formula (I), is new.    M'=Group 8 metal;    X and X1=anionic ligands;    L'=neutral two electron donor;    L1=N, O, P, or S (preferably N, or O);    R'=optionally substituted 1-30C hydrocarbyl;    G1 and R1=H, or optionally substituted 1-30C hydrocarbyl;    G'=H, halo, or optionally substituted 1-30C hydrocarbyl.    An INDEPENDENT CLAIM is included for process (P1) for producing alpha-olefin (preferably 4-24C linear alpha-olefin) involving:    (1) process (A): contacting a feed material (such as a feed oil) with the catalyst compound (I);    (2) process (B): contacting a triacylglyceride with an alkene and the catalyst compound (I), where preferably the alpha olefin produced has at least one more carbon atom than the alkene; or    (3) process (C): contacting an unsaturated fatty acid, or unsaturated fatty acid ester and/or unsaturated fatty acid alkyl ester; or a triacylglyceride, fatty acid, fatty acid alkyl ester, and/or fatty acid ester derived from seed oil, with an alkene and the catalyst compound (I), where preferably the alpha olefin produced has at least one more carbon atom than the alkene.